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In the present thesis the MBE growth and sample characterization of HgTe structures is investigated
and discussed. Due to the first experimental discovery of the quantum Spin Hall effect
(QSHE) in HgTe quantum wells, this material system attains a huge interest in the spintronics
society. Because of the long history of growing Hg-based heterostructures here at the Experimentelle
Physik III in Würzburg, there are very good requirements to analyze this material
system more precisely and in new directions. Since in former days only doped HgTe quantum
wells were grown, this thesis deals with the MBE growth in the (001) direction of undoped
HgTe quantum wells, surface located quantum wells and three dimensional bulk layers. All
Hg-based layers were grown on CdTe substrates which generate strain in the layer stack and
provide therefore new physical effects. In the same time, the (001) CdTe growth was investigated
on n-doped (001) GaAs:Si because the Japanese supplier of CdTe substrates had a
supply bottleneck due to the Tohoku earthquake and its aftermath in 2011.
After a short introduction of the material system, the experimental techniques were demonstrated
and explained explicitly. After that, the experimental part of this thesis is displayed.
So, the investigation of the (001) CdTe growth on (001) GaAs:Si is discussed in chapter 4.
Firstly, the surface preparation of GaAs:Si by oxide desorption is explored and analyzed.
Here, rapid thermal desorption of the GaAs oxide with following cool down in Zn atmosphere
provides the best results for the CdTe due to small holes at the surface, while e.g. an atomic
flat GaAs buffer deteriorates the CdTe growth quality. The following ZnTe layer supplies the
(001) growth direction of the CdTe and exhibits best end results of the CdTe for 30 seconds
growth time at a flux ratio of Zn/Te ~ 1/1.2. Without this ZnTe layer, CdTe will grow in the
(111) direction. However, the main investigation is here the optimization of the MBE growth
of CdTe. The substrate temperature, Cd/Te flux ratio and the growth time has to be adjusted
systematically. Therefore, a complex growth process is developed and established. This optimized
CdTe growth process results in a RMS roughness of around 2.5 nm and a FWHM value
of the HRXRD w-scan of 150 arcsec. Compared to the literature, there is no lower FWHM
value traceable for this growth direction. Furthermore, etch pit density measurements show
that the surface crystallinity is matchable with the commercial CdTe substrates (around 1x10^4
cm^(-2)). However, this whole process is not completely perfect and offers still room for improvements.
The growth of undoped HgTe quantum wells was also a new direction in research in contrast
to the previous n-doped grown HgTe quantum wells. Here in chapter 5, the goal of very low
carrier densities was achieved and therefore it is now possible to do transport experiments in
the n - and p - region by tuning the gate voltage. To achieve this high sample quality, very precise
growth of symmetric HgTe QWs and their HRXRD characterization is examined. Here,
the quantum well thickness can now determined accurate to under 0.3 nm. Furthermore, the transport analysis of different quantum well thicknesses shows that the carrier density and
mobility increase with rising HgTe layer thickness. However, it is found out that the band
gap of the HgTe QW closes indirectly at a thickness of 11.6 nm. This is caused by the tensile
strained growth on CdTe substrates. Moreover, surface quantum wells are studied. These
quantum wells exhibit no or a very thin HgCdTe cap. Though, oxidization and contamination
of the surface reduces here the carrier mobility immensely and a HgCdTe layer of around 5 nm
provides the pleasing results for transport experiments with superconductors connected to the
topological insulator [119]. A completely new achievement is the realization of MBE growth
of HgTe quantum wells on CdTe/GaAs:Si substrates. This is attended by the optimization of
the CdTe growth on GaAs:Si. It exposes that HgTe quantum wells grown in-situ on optimized
CdTe/GaAs:Si show very nice transport data with clear Hall plateaus, SdH oscillations, low
carrier densities and carrier mobilities up to 500 000 cm^2/Vs. Furthermore, a new oxide etching
process is developed and analyzed which should serve as an alternative to the standard
HCl process which generates volcano defects at some time. However, during the testing time
the result does not differ in Nomarski, HRXRD, AFM and transport measurements. Here,
long-time tests or etching and mounting in nitrogen atmosphere may provide new elaborate
results.
The main focus of this thesis is on the MBE growth and standard characterization of HgTe bulk
layers and is discussed in chapter 6. Due to the tensile strained growth on lattice mismatched
CdTe, HgTe bulk opens up a band gap of around 22 meV at the G-point and exhibits therefore
its topological surface states. The analysis of surface condition, roughness, crystalline quality,
carrier density and mobility via Nomarski, AFM, XPS, HRXRD and transport measurements
is therefore included in this work. Layer thickness dependence of carrier density and mobility
is identified for bulk layer grown directly on CdTe substrates. So, there is no clear correlation
visible between HgTe layer thickness and carrier density or mobility. So, the carrier density is
almost constant around 1x10^11 cm^(-2) at 0 V gate voltage. The carrier mobility of these bulk
samples however scatters between 5 000 and 60 000 cm^2/Vs almost randomly. Further experiments
should be made for a clearer understanding and therefore the avoidance of unusable
bad samples.But, other topological insulator materials show much higher carrier densities and
lower mobility values. For example, Bi2Se3 exhibits just density values around 1019 cm^(-2)
and mobility values clearly below 5000 cm2/Vs. The carrier density however depends much
on lithography and surface treatment after growth. Furthermore, the relaxation behavior and
critical thickness of HgTe grown on CdTe is determined and is in very good agreement with
theoretical prediction (d_c = 155 nm). The embedding of the HgTe bulk layer between HgCdTe
layers created a further huge improvement. Similar to the quantum well structures the carrier
mobility increases immensely while the carrier density levels at around 1x10^11 cm^(-2) at 0
V gate voltage as well. Additionally, the relaxation behavior and critical thickness of these
barrier layers has to be determined. HgCdTe grown on commercial CdTe shows a behavior as
predicted except the critical thickness which is slightly higher than expected (d_c = 850 nm).
Otherwise, the relaxation of HgCdTe grown on CdTe/GaAs:Si occurs in two parts. The layer
is fully strained up to 250 nm. Between 250 nm and 725 nm the HgCdTe film starts to relax
randomly up to 10 %. The relaxation behavior for thicknesses larger than 725 nm occurs than
linearly to the inverse layer thickness. A explanation is given due to rough interface conditions
and crystalline defects of the CdTe/GaAs:Si compared to the commercial CdTe substrate. HRXRD and AFM data support this statement. Another point is that the HgCdTe barriers protect the active HgTe layer and because of the high carrier mobilities the Hall measurements provide new transport data which have to be interpreted more in detail in the future. In addition, HgTe bulk samples show very interesting transport data by gating the sample from the top and the back. It is now possible to manipulate the carrier densities of the top and bottom surface states almost separately. The back gate consisting of the n-doped GaAs substrate and the thick insulating CdTe buffer can tune the carrier density for Delta(n) ~ 3x10^11 cm^(-2). This is sufficient to tune the Fermi energy from the p-type into the n-type region [138].
In this thesis it is shown that strained HgTe bulk layers exhibit superior transport data by embedding between HgCdTe barrier layers. The n-doped GaAs can here serve as a back gate.
Furthermore, MBE growth of high crystalline, undoped HgTe quantum wells shows also new
and extended transport output. Finally, it is notable that due to the investigated CdTe growth
on GaAs the Hg-based heterostructure MBE growth is partially independent from commercial
suppliers.
Exploring the transport properties of the three-dimensional topological insulator material HgTe
(2015)
In the present thesis the transport properties of strained bulk HgTe devices are investigated. Strained HgTe forms a 3D TI and is of special interest for studying topological surface states, since it can be grown by MBE in high crystal quality. The low defect density leads to considerable mobility values, well above the mobilities of other TI materials. However, strained HgTe has a small band gap of ca. 20 meV. With respect to possible applications the question is important, under which conditions the surface transport occurs. To answer this question, the HgTe devices are investigated at dilution refrigerator temperatures (T<100 mK) in high magnetic fields of different orientation. The influence of top and back gate electrodes as well as surface protecting layers is discussed.
On the basis of an analysis of the quantum Hall behaviour it is shown that transport is dominated by the topological surface states in a surprisingly large parameter range. A dependence on the applied top gate voltage is presented for the topological surface states. It enables the first demonstration of an odd integer QHE sequence from the surfaces perpendicular to the magnetic field. Furthermore, the p-type QHE from the surface states is observed for the first time in any 3D TI. This is achieved in samples of high surface quality. It is concluded from the gate response that the screening behaviour in 3D TI devices is non-trivial. The transport data are qualitatively analysed by means of intuitive theoretical models.
The combination of a topological insulator (TI) and a superconductor (S), which together
form a TI/S interface, is expected to influence the possible surface states in the
TI. It is of special interest, if the theoretical prediction of zero energy Majorana states
in this system is verifiable. This thesis presents the experimental realization of such
an interface between the TI strained bulk HgTe and the S Nb and studies if the afore
mentioned expectations are met.
As these types of interfaces were produced for the first time the initial step was
to develop a new lithographic process. Optimization of the S deposition technique as
well as the application of cleaning processes allowed for reproducible fabrication of
structures. In parallel the measurement setup was upgraded to be able to execute the
sensitive measurements at low energy. Furthermore several filters have been implemented
into the system to reduce high frequency noise and the magnetic field control
unit was additionally replaced to achieve the needed resolution in the μT range.
Two kinds of basic geometries have been studied: Josephson junctions (JJs) and
superconducting quantum interference devices (SQUIDs). A JJ consists of two Nb contacts
with a small separation on a HgTe layer. These S/TI/S junctions are one of the
most basic structures possible and are studied via transport measurements. The transport
through this geometry is strongly influenced by the behavior at the two S/TI
interfaces. In voltage dependent differential resistance measurements it was possible
to detect multiple Andreev reflections in the JJ, indicating that electrons and holes are
able to traverse the HgTe gap between both interfaces multiple times while keeping
phase coherence. Additionally using BTK theory it was possible to extract the interface
transparency of several junctions. This allowed iterative optimization for the highest
transparency via lithographic improvements at these interfaces. The increased transparency
and thus the increased coupling of the Nb’s superconductivity to the HgTe
results in a deeper penetration of the induced superconductivity into the HgTe. Due
to this strong coupling it was possible to enter the regime, where a supercurrent is
carried through the complete HgTe layer. For the first time the passing of an induced
supercurrent through strained bulk HgTe was achieved and thus opened the area for
detailed studies. The magnetic dependence of the supercurrent in the JJ was recorded,
which is also known as a Fraunhofer pattern. The periodicity of this pattern in magnetic
field compared to the JJ geometry allowed to conclude how the junction depends
on the phase difference between both superconducting contacts. Theoretical calculations
predicted a phase periodicity of 4p instead of 2p, if a TI is used as weak link
material between the contacts, due to the presence of Majorana modes. It could clearly
be shown that despite the usage of a TI the phase still was 2p periodic. By varying
further influencing factors, like number of modes and phase coherence length in the
junction, it might still be possible to reach the 4p regime with bound Majorana states
in the future. A good candidate for further experiments was found in capped HgTe
samples, but here the fabrication process still has to be developed to the same quality
as for the uncapped HgTe samples.
The second type of geometry studied in this thesis was a DC-SQUID, which consists
of two parallel JJs and can also be described as an interference device between two JJs.
The DC-SQUID devices were produced in two configurations: The symmetric SQUID,
where both JJs were identical, and the asymmetric SQUID, where one JJ was not linear,
but instead has a 90° bent. These configurations allow to test, if the predicted
uniformity of the superconducting band gap for induced superconductivity in a TI
is valid. While the phase of the symmetric SQUID is not influenced by the shape of
the band gap, the asymmetric SQUID would be in phase with the symmetric SQUID
in case of an uniform band gap and out of phase if p- or d-wave superconductivity
is dominating the transport, due to the 90° junction. As both devices are measured
one after another, the problem of drift in the coil used to create the magnetic field has
to be overcome in order to decide if the oscillations of both types of SQUIDs are in
phase. With an oscillation period of 0.5 mT and a drift rate in the range of 5.5 μT/h
the measurements on both configurations have to be conducted in a few hours. Only
then the total shift is small enough to compare them with each other. For this to be
possible a novel measurement system based on a real time micro controller was programmed,
which allows a much faster extraction of the critical current of a device. The
measurement times were reduced from days to hours, circumventing the drift problems
and enabling the wanted comparison. After the final system optimizations it has
been shown that the comparison should now be possible. Initial measurements with
the old system hinted that both types of SQUIDs are in phase and thus the expected
uniform band gap is more likely. With all needed optimizations in place it is now up
to the successors of this project to conclusively prove this last point.
This thesis has proven that it is possible to induce superconductivity in strained
bulk HgTe. It has thus realized the most basic sample geometry proposed by Fu and
Kane in 2008 for the appearance of Majorana bound states. Based on this work it is
now possible to further explore induced superconductivity in strained bulk HgTe to
finally reach a regime, where the Majorana states are both stable and detectable.
Topological insulators belong to a new quantum state of matter that is currently one of
the most recognized research fields in condensed matter physics. Strained bulk HgTe
and HgTe/HgCdTe quantum well structures are currently one of few topological insulator
material systems suitable to be studied in transport experiments. In addition
HgTe quantum wells provide excellent requirements for the conduction of spintronic
experiments. A fundamental requirement for most experiments, however, is to reliably
pattern these heterostructures into advanced nano-devices. Nano-lithography on this
material system proves to be challenging because of inherent temperature limitations,
its high reactivity with various metals and due to its properties as a topological insulator.
The current work gives an insight into why many established semiconductor
lithography processes cannot be easily transferred to HgTe while providing alternative
solutions. The presented developments include novel ohmic contacts, the prevention
of metal sidewalls and redeposition fences in combination with low temperature
(80 °C) lithography and an adapted hardmask lithography process utilizing a sacrificial
layer. In addition we demonstrate high resolution low energy (2.5 kV) electron beam
lithography and present an alternative airbridge gating technique. The feasibility of
nano-structures on HgTe quantum wells is exemplarily verified in two separate transport
experiments. We are first to realize physically etched quantum point contacts
in HgTe/HgCdTe high mobility 2DEGs and to prove their controllability via external
top-gate electrodes. So far quantum point contacts have not been reported in TI
materials. However, these constrictions are part of many proposals to probe the nature
of the helical quantum spin Hall edge channels and are suggested as injector and
detector devices for spin polarized currents. To confirm their functionality we performed
four-terminal measurements of the point contact conductance as a function of
external gate voltage. Our measurements clearly exhibit quantized conductance steps
in 2e2/h, which is a fundamental characteristic of quantum point contacts. Furthermore
we conducted measurements on the formation and control of collimated electron beams, a key feature to realize an all electrical spin-optic device. In a second study
several of the newly developed lithography techniques were implemented to produce
arrays of nano-wires on inverted and non-inverted HgTe quantum well samples. These
devices were used in order to probe and compare the weak antilocalization (WAL) in
these structures as a function of magnetic field and temperature. Our measurements
reveal that the WAL is almost an order of magnitude larger in inverted samples. This
observation is attributed to the Dirac-like dispersion of the energy bands in HgTe quantum
wells. The described lithography has already been successfully implemented and
adapted in several published studies. All processes have been optimized to guarantee
a minimum effect on the heterostructure’s properties and the sample surface, which is
especially important for probing the topological surface states of strained HgTe bulk
layers. Our developments therefore serve as a base for continuous progress to further
establish HgTe as a topological insulator and give access to new experiments.
Molecular Beam Epitaxy and Characterization of Bi-Based V\(_2\)VI\(_3\) Topological Insulators
(2016)
The present thesis is addressed to the growth and characterization of Bi-based V2VI3 topological insulators (TIs). The TIs were grown by molecular beam epitaxy (MBE) on differently passivated Si(111) substrates, as well as InP(111) substrates. This allows the study of the influence of the substrate on the structural and electrical properties of the TIs.
The Bi2Se3 layers show a change of mosaicity-tilt and -twist for growth on the differently prepared Si(111) substrates, as well as a significant increase of crystalline quality for growth on the lateral nearly lattice matched InP(111). The rocking curve FWHMs observed for thick layers grown on InP are comparable to these of common zincblende layers, which are close to the resolution limit of standard high resolution X-ray diffraction (HRXRD) setups. The unexpected high structural crystalline quality achieved in this material system is remarkable due to the presence of weak van der Waals bonds between every block of five atomic layers, i.e. a quintuple layer (QL), in growth direction.
In addition to the mosaicity also twin domains, present in films of the V2VI3 material system, are studied. The twin defects are observed in Bi2Se3 layers grown on Si(111) and lattice matched InP(111) suggesting that the two dimensional surface lattice of the substrates can not determine the stacking order ABCABC... or ACBACB... in locally separated growth seeds. Therefore the growth on misoriented and rough InP(111) is analyzed.
The rough InP(111) with its facets within a hollow exceeding the height of a QL is able to provide its stacking information to the five atomic layers within a QL. By varying the roughness of the InP substrate surface, due to thermal annealing, the influence on the twinning within the layer is confirmed resulting in a complete suppression of twin domains on rough InP(111).
Focusing on the electrical properties of the Bi2Se3 films, the increased structural quality for films grown on lattice matched flat InP(111)B results in a marginal reduction of carrier density by about 10% compared to the layers grown on H-passivated Si(111), whereas the suppression of twin domains for growth on rough InP(111)B resulted in a reduction of carrier density by an order of magnitude. This implies, that the twin domains are a main crystal defect responsible for the high carrier density in the presented Bi2Se3 thin films.
Besides the binary Bi2Se3 also alloys with Sb and Te are fabricated to examine the influence of the compound specific point defects on the carrier density. Therefore growth series of the ternary materials Bi2Te(3-y)Se(y), Bi(2-x)Sb(x)Se3, and Bi(2-x)Sb(x)Te3, as well as the quaternary Bi(2-x)Sb(x)Te(3-y)Se(y) are studied.
To further reduce the carrier density of twin free Bi2Se3 layers grown on InP(111)B:Fe a series of Bi(2-x)Sb(x)Se3 alloys were grown under comparable growth conditions. This results in a reduction of the carrier density with a minimum in the composition range of about x=0.9-1.0.
The Bi(2-x)Sb(x)Te3 alloys exhibit a pn-transition, due to the dominating n-type and p-type point defects in its binary compounds, which is determined to reduce the bulk carrier density enabling the study the TI surface states. This pn-transition plays a significant role in realizing predicted applications and exotic effects, such as the quantum anomalous Hall effect.
The magnetic doping of topological insulators with transition metals is studied by incorporating Cr and V in the alloy Bi(2-x)Sb(x)Te3 by codeposition. The preferential incorporation of Cr on group-V sites is confirmed by EDX and XRD, whereas the incorporation of Cr reduces the crystalline quality of the layer. Magnetotransport measurements of the Cr-doped TIs display an anomalous Hall effect confirming the realization of a magnetic TI thin film. The quantum anomalous Hall effect is observed in V-doped Bi(2-x)Sb(x)Te3, where the V-doping results in higher Curie temperatures, as well as higher coercive fields compared to the Cr-doping of the TIs.
Moreover the present thesis contributes to the understanding of the role of the substrate concerning the crystalline quality of van der Waals bonded layers, such as the V2VI3 TIs, MoS2 and WoTe2. Furthermore, the fabrication of the thin film TIs Bi(2-x)Sb(x)Te(3-y)Se(y) in high crystalline quality serves as basis to explore the physics of topological insulators.
A novel growth method has been developed, allowing for the growth of strained HgTe shells on CdTe nanowires (NWs). The growth of CdTe-HgTe core-shell NWs required high attention in controlling basic parameters like substrate temperature and the intensity of supplied material fluxes. The difficulties in finding optimized growth conditions have been successfully overcome in this work.
We found the lateral redistribution of liquid growth seeds with a ZnTe growth start to be crucial to trigger vertical CdTe NW growth. Single crystalline zinc blende CdTe NWs grew, oriented along [111]B. The substrate temperature was the most critical parameter to achieve straight and long wires. In order to adjust it, the growth was monitored by reflection high-energy electron diffraction, which was used for fine tuning of the temperature over time in each growth run individually. For optimized growth conditions, a periodic diffraction pattern allowed for the detailed analysis of atomic arrangement on the surfaces and in the bulk. The ability to do so reflected the high crystal quality and ensemble uniformity of our CdTe NWs. The NW sides were formed by twelve stable, low-index crystalline facets. We observed two types stepped and polar sides, separated by in total six flat and non-polar facets.
The high crystalline quality of the cores allowed to grow epitaxial HgTe shells around. We reported on two different heterostructure geometries. In the first one, the CdTe NWs exhibit a closed HgTe shell, while for the second one, the CdTe NWs are overgrown mainly on one side. Scanning electron microscopy and scanning transmission electron microscopy confirmed, that many of the core-shell NWs are single crystalline zinc blende and have a high uniformity. The symmetry of the zinc blende unit cell was reduced by residual lattice strain. We used high-resolution X-ray diffraction to reveal the strain level caused by the small lattice mismatch in the heterostructures. Shear strain has been induced by the stepped hetero-interface, thereby stretching the lattice of the HgTe shell by 0.06 % along a direction oriented with an angle of 35 ° to the interface.
The different heterostructures obtained, were the base for further investigation of quasi-one-dimensional crystallites of HgTe. We therefore developed methods to reliably manipulate, align, localize and contact individual NWs, in order to characterize the charge transport in our samples. Bare CdTe cores were insulating, while the HgTe shells were conducting. At low temperature we found the mean free path of charge carriers to be smaller, but the phase coherence length to be larger than the sample size of several hundred nanometers. We observed universal conductance fluctuations and therefore drew the conclusion, that the trajectories of charge carriers are defined by elastic backscattering at randomly distributed scattering sites. When contacted with superconducting leads, we saw induced superconductivity, multiple Andreev reflections and the associated excess current. Thus, we achieved HgTe/superconductor interfaces with high interfacial transparency.
In addition, we reported on the appearance of peaks in differential resistance at Delta/e for HgTe-NW/superconductor and 2*Delta/e for superconductor/HgTe-NW/superconductor junctions, which is possibly related to unconventional pairing at the HgTe/superconductor interface. We noticed that the great advantage of our self-organized growth is the possibility to employ the metallic droplet, formerly seeding the NW growth, as a superconducting contact. The insulating wire cores with a metallic droplet at the tip have been overgrown with HgTe in a fully in-situ process. A very high interface quality was achieved in this case.
Neue Erkenntnisse über elektronische Eigenschaften von Festkörpern legen den Grundstein für innovative Anwendungen der Zukunft. Von zentraler Bedeutung sind insbesondere die Eigenschaften der Elektronenspins. Um diese besser zu verstehen, befasst sich die vorliegende Arbeit mit der experimentellen Analyse der elektronischen Struktur von topologischen Isolatoren (Sb$_2$Te$_3$ , Bi$_2$Se$_x$Te$_{3−x}$, Bi$_{1.5}$Sb$_{0.5}$Te$_{1.8}$Se$_{1.2} und Bi$_{1.4}$Sb$_{1.1}$Te$_{2.2}$S$_{0.3}$) und Kristallen mit starker Spin-Bahn-Wechselwirkung (BiTeI) mittels Photoelektronenspektroskopie. Zu Beginn werden die zum Verständnis dieser Arbeit benötigten Grundlagen erklärt sowie die unterschiedlichen zum Einsatz kommenden Techniken eingeführt. Der Hauptteil der Arbeit teilt sich in drei Forschungsschwerpunkte. Der erste Teil befasst sich mit den elektronischen Eigenschaften der Valenzbandstruktur von Sb2Te3 und den auftretenden Oberflächenzuständen. Durch gezielte Variation der Energie der anregenden Strahlung wird der Charakter der Wellenfunktion des topologischen Oberflächenzustands und dessen Wechselwirkung mit Valenzzuständen erforscht. Dabei spielt die Topologie der Volumenbandstruktur eine grundlegende Rolle. Der zusätzliche Vergleich zu Photoemissionsrechnungen ermöglicht detaillierte Einblicke in die Wechselwirkung zwischen Oberflächen- und Volumenzuständen und gibt Aufschluss darüber, wie diese vermittelt werden.
Im zweiten Abschnitt wird durch die Analyse des gemessenen Photoelektronenspins das Zusammenspiel der Spintextur des Grundzustands und Endzuständen in Bi2Te3 untersucht. Dabei treten, im Gegensatz zu Grundzustandsrechnungen, Radialkomponenten des Polarisationsvektors in nichtsymmetrischer Messgeometrie auf. Sowohl deren Energieabhängigkeit als auch deren Auftreten in Photoemissionsrechnungen (1-Schritt-Modell) deutet darauf hin, dass diese ihren Ursprung in Übergangsmatrixelementen des Photoemissionsprozesses haben. Dieses Ergebnis wird mit Spinpolarisationsmessungen am Oberflächenzustand des nicht-topologischen Schichtsystems BiTeI verglichen.
Im dritten Teil werden Auswirkungen unterschiedlicher Manipulationen der untersuchten Materialien auf deren elektronische Eigenschaften beschrieben. Die Adsorption von Bruchteilen einer monoatomaren Lage des Alkalimetalls Caesium auf die Oberfläche des topologischen Isolators Sb2Te3 wird systematisch untersucht. Dadurch kann dessen intrinsische p-Dotierung teilweise abgebaut werden, wobei die Valenzbandstruktur trotz der Reaktivität des Adsorbats intakt bleibt. Des Weiteren werden Auswirkungen von Änderungen der Kristallstöchiometrie durch Volumendotierung vergleichend diskutiert.
Ausblickend befasst sich das Kapitel mit dem Verhalten geringer Mengen ferromagnetischer
Materialen (Fe, Ni) auf den Oberflächen der topologischen Isolatoren. Für die verschiedenen Adsorbate werden Trends aufgezeigt, die von Temperatur und Zusammensetzung des Substratkristalls abhängen.
Im Rahmen dieser Arbeit wurde ein Rastertunnelmikroskop (STM) für Messungen bei tiefen Temperaturen und hohen Magnetfeldern konzipiert und aufgebaut. Die Probentemperatur kann dabei auf bis zu 1.4\,Kelvin reduziert werden, was spektroskopische Messungen mit extrem hoher Energieauflösung ermöglicht. Die thermische Verbreiterung spektroskopischer Merkmale liegt somit im Bereich eines Milli-Elektronenvolts, wie durch den Fit der Bandlücke eines supraleitenden Materials demonstriert wird. Ein linearer Bewegungsmechanismus ermöglicht die Positionierung des STM-Körpers innerhalb einer supraleitenden Spule, in der Magnetfelder von bis zu 12.5\,Tesla senkrecht zur Probenoberfläche erzeugt werden können. Das System erlaubt des Weiteren den Wechsel von Spitzen und Proben innerhalb des Kryostaten sowie das Aufdampfen von Einzelatomen auf die kalte Probenoberfläche ohne die Probe aus dem STM zu entfernen. Um den Einfluss mechanischer Vibrationen zu minimieren wurde ein innovatives Feder-Dämpfungssystem entwickelt, dass eine Stabilität des Tunnelkontakts von bis zu einem Pikometer gewährleistet. \\
\noindent Der zweite Teil dieser Arbeit präsentiert die Ergebnisse von STM-Messungen auf Antimon-Tellurid (Sb_{2}Te_{3}). Sb_{2}Te_{3}\, gehört zur relativ neu entdeckten Materialklasse der Topologischen Isolatoren (TI). Diese Verbindungen besitzen auf ihren Oberflächen Zustände mit linearer Dispersion, die durch die Zeitumkehr-Invarianz geschützt werden. Fokus unserer Messungen ist dabei der Einfluss eines magnetischen Feldes auf die Eigenschaften eines derartigen unkonventionellen 2D-Elektronengases. Dazu wurde die Entstehung von Landau Level (LL) innerhalb eines Magnetfelds genau untersucht. Die zwei in dieser Arbeit untersuchten Hauptaspekte sind: \medskip
\noindent(i) Die energetische Verbreiterung, die Rückschlüsse auf die Lebensdauer zulässt\\
(ii) Die örtliche Fluktuation. \medskip
\noindent Erstaunlicherweise kann die gemessene Verbreiterung der Landau Resonanzen nicht mit gängigen Mechanismen der Lebenszeit-Verbreiterung erklärt werden. Aus diesem Grund wird eine alternative Interpretation basierend auf der Heissenbergschen Unschärferelation vorgestellt, die im guten Einklang mit den von uns gewonnenen Daten steht. Des Weiteren zeigen örtlich aufgelöste Messungen systematische Abweichungen in der Dirac-Geschwindigkeit positiver und negativer Landau Resonanzen. Diese Fluktuationen stehen dabei in direktem Zusammenhang mit Änderungen im lokalen chemischen Potential. Da die physikalischen Ursachen dieser Abweichung im Rahmen dieser Arbeit nicht zweifelsfrei geklärt werden konnten, werden im letzten Teil die zugrundeliegenden Messergebnisse vorgestellt und mögliche Erklärungen des Verhaltens präsentiert.
The subject of this thesis is the control of strain in HgTe thin-film crystals. Such systems are members of the new class of topological insulator materials and therefore of special research interest. A major task was the experimental control of the strain in the HgTe films. This was achieved by a new epitaxial approach and confirmed by cristallographic analysis and magneto-transport measurements.
In this work, strain was induced in thin films by means of coherent epitaxy on substrate crystals. This means that the film adopts the lattice constant of the substrate in the plane of the substrate-epilayer interface. The level of strain is determined by the difference between the strain-free lattice constants of the substrate and epilayer material (the so-called lattice mismatch). The film responds to an in-plane strain with a change of its lattice constant perpendicular to the interface. This relationship is crucial for both the correct interpretation of high resolution X-ray diffraction (HRXRD) measurements, and the precise determination of the band dispersion. The lattice constant of HgTe is smaller than the lattice constant of CdTe. Therefore, strain in HgTe is tensile if it is grown on a CdTe substrate. In principle, compressive strain can be achieved by using an appropriate \(\text{Cd}_{1-x}\text{Zn}_{x}\text{Te}\) substrate. This concept was modified and applied in this work.
Epilayers have been fabricated by molecular-beam epitaxy (MBE). The growth of thick buffer layers of CdTe on GaAs:Si was established as an alternative to commercial CdTe and \(text{Cd}_{0.96}\text{Zn}_{0.04}\text{Te}\) substrates. The growth conditions have been optimized by an analysis of atomic force microscopy and HRXRD studies. HRXRD measurements reveal a power-law increase of the crystal quality with increasing thickness. Residual strain was found in the buffer layers, and was attributed to a combination of finite layer thickness and mismatch of the thermal expansion coefficients of CdTe and GaAs. In order to control the strain in HgTe epilayers, we have developed a new type of substrate with freely adjustable lattice constant.
CdTe-\(\text{Cd}_{0.5}\text{Zn}_{0.5}\text{Te}\) strained-layer-superlattices have been grown by a combination of MBE and atomic-layer epitaxy (ALE), and have been analyzed by HRXRD. ALE of the \(\text{Cd}_{0.5}\text{Zn}_{0.5}\text{Te}\) layer is self-limiting to one monolayer, and the effective lattice constant can be controlled reproducibly and straightforward by adjusting the CdTe layer thickness. The crystal quality has been found to degrade with increasing Zn-fraction. However, the effect is less drastic compared to single layer \(\text{Cd}_{1-x}\text{Zn}_{x}\text{Te}\) solid solutions. HgTe quantum wells (QWs) sandwiched in between CdHgTe barriers have been fabricated in a similar fashion on superlattices and conventional CdTe and \(\text{Cd}_{0.96}\text{Zn}_{0.04}\text{Te}\) substrates. The lower critical thickness of the CdHgTe barrier material grown on superlattice substrates had to be considered regarding the sample design. The electronic properties of the QWs depend on the strain and thickness of the QW. We have determined the QW thickness with an accuracy of \(\pm\)0.5 nm by an analysis of the beating patterns in the thickness fringes of HRXRD measurements and X-ray reflectometry measurements. We have, for the first time, induced compressive strain in HgTe QWs by an epitaxial technique (i.e. the effective lattice constant of the superlattice is lower compared to the lattice constant of HgTe). The problem of the lattice mismatch between superlattice and barriers has been circumvented by using CdHgTe-ZnHgTe superlattices instead of CdHgTe as a barrier material. Furthermore, the growth of compressively strained HgTe bulk layers (with a thickness of at least 50 nm) was demonstrated as well.
The control of the state of strain adds a new degree of freedom to the design of HgTe epilayers, which has a major influence on the band structure of QWs and bulk layers. Strain in bulk layers lifts the degeneracy of the \(\Gamma_8\) bands at \(\mathbf{k}=0\). Tensile strain opens an energy gap, compressive strain shifts the touching points of the valence- and conduction band to positions in the Brillouin zone with finite \(\mathbf{k}\). Such a situation has been realized for the first time in the course of this work. For QWs in the inverted regime, it is demonstrated that compressive strain can be used to significantly enhance the thermal energy gap of the two-dimensional electron gas (2DEG). In addition, semi-metallic and semiconducting behavior is expected in wide QWs, depending on the state of strain. An examination of the temperature dependence of the subband ordering in QWs revealed that the band gap is only temperature-stable for appropriate sample parameters and temperature regimes. The band inversion is always lifted for sufficiently high temperatures.
A large number of models investigate the influence of the band gap on the stability of the quantum-spin-Hall (QSH) effect. An enhancement of the stability of QSH edge state conductance is expected for enlarged band gaps. Furthermore, experimental studies on the temperature dependence of the QSH conductance are in contradiction to theoretical predictions. Systematic studies of these aspects have become feasible based on the new flexibility of the sample design.
Detailed low-temperature magnetotransport studies have been carried out on QWs and bulk layers. For this purpose, devices have been fabricated lithographically, which consist of two Hall-bar geometries with different dimensions. This allows to discriminate between conductance at the plane of the 2DEG and the edge of the sample. The Fermi energy in the 2DEG has been adjusted by means of a top gate electrode. The strain-induced transition from semi-metallic to semiconducting characteristics in wide QWs was shown. The magnitude of the semi-metallic overlap of valence- and conduction band was determined by an analysis of the two-carrier conductance and is in agreement with band structure calculations. The band gap of the semiconducting sample was determined by measurements of the temperature dependence of the conductance at the charge-neutrality point. Agreement with the value expected from theory has been achieved for the first time in this work. The influence of the band gap on the stability of QSH edge state conductance has been investigated on a set of six samples. The band gap of the set spans a range of 10 to 55 meV. The latter value has been achieved in a highly compressively strained QW, has been confirmed by temperature-dependent conductance measurements, and is the highest ever reported in the inverted regime. Studies of the carrier mobility reveal a degradation of the sample quality with increasing Zn-fraction in the superlattice, in agreement with HRXRD observations. The enhanced band gap does not suppress scattering mechanisms in QSH edge channels, but lowers the conductance in the plane of the 2DEG. Hence, edge state conductance is the dominant conducting process even at elevated temperatures. An increase in conductance with increasing temperature has been found, in agreement with reports from other groups. The increase follows a power-law dependency, the underlying physical mechanism remains open. A cause for the lack of an increase of the QSH edge state conductance with increasing energy gap has been discussed. Possibly, the sample remains insulating even at finite carrier densities, due to localization effects. The measurement does not probe the QSH edge state conductance at the situation where the Fermi energy is located in the center of the energy gap, but in the regime of maximized puddle-driven scattering. In a first set of measurements, it has been shown that the QSH edge state conductance can be influenced by hysteretic charging effects of trapped states in the insulating dielectric. A maximized conductance of \(1.6\ \text{e}^2/\text{h}\) was obtained in a \(58\ \mu\text{m}\) edge channel. Finally, measurements on three dimensional samples have been discussed. Recent theoretical works assign compressively strained HgTe bulk layers to the Weyl semi-metal class of materials. Such layers have been synthesized and studied in magnetotransport experiments for the first time. Pronounced quantum-Hall- and Shubnikov-de-Haas features in the Hall- and longitudinal resistance indicate two-dimensional conductance on the sample surface. However, this conductance cannot be assigned definitely to Weyl surface states, due to the inversion of \(\Gamma_6\) and \(\Gamma_8\) bands. If a magnetic field is aligned parallel to the current in the device, a decrease in the longitudinal resistance is observed with increasing magnetic field. This is a signature of the chiral anomaly, which is expected in Weyl semi-metals.
This thesis describes the studies of topological superconductivity, which is predicted to
emerge when pair correlations are induced into the surface states of 2D and 3D topolog-
ical insulators (TIs). In this regard, experiments have been designed to investigate the
theoretical ideas first pioneered by Fu and Kane that in such system Majorana bound
states occur at vortices or edges of the system [Phys. Rev. Lett. 100, 096407 (2008), Phys.
Rev. B 79, 161408 (2009)]. These states are of great interest as they constitute a new
quasiparticle which is its own antiparticle and can be used as building blocks for fault
tolerant topological quantum computing.
After an introduction in chapter 1, chapter 2 of the thesis lays the foundation for the
understanding of the field of topology in the context of condensed matter physics with a
focus on topological band insulators and topological superconductors. Starting from a
Chern insulator, the concepts of topological band theory and the bulk boundary corre-
spondence are explained. It is then shown that the low energy Hamiltonian of mercury
telluride (HgTe) quantum wells of an appropriate thickness can be written as two time
reversal symmetric copies of a Chern insulator. This leads to the quantum spin Hall effect.
In such a system, spin-polarized one dimensional conducting states form at the edges
of the material, while the bulk is insulating. This concept is extended to 3D topological
insulators with conducting 2D surface states. As a preliminary step to treating topological
superconductivity, a short review of the microscopic theory of superconductivity, i.e. the
theory of Bardeen, Cooper, and Shrieffer (BCS theory) is presented. The presence of
Majorana end modes in a one dimensional superconducting chain is explained using the
Kitaev model. Finally, topological band insulators and conventional superconductivity
are combined to effectively engineer p-wave superconductivity. One way to investigate
these states is by measuring the periodicity of the phase of the Josephson supercurrent
in a topological Josephson junction. The signature is a 4π-periodicity compared to the
2π-periodicity in conventional Josephson junctions. The proof of the presence of this
effect in HgTe based Josephson junction is the main goal of this thesis and is discussed in
chapters 3 to 6.
Chapter 3 describes in detail the transport of a 3D topological insulator based weak
link under radio-frequency radiation. The chapter starts with a review of the state of
research of (i) strained HgTe as 3D topological insulator and (ii) the progress of induc-
ing superconducting correlations into the topological surface states and the theoretical
predictions of 3D TI based Josephson junctions. Josephson junctions based on strained
HgTe are successfully fabricated. Before studying the ac driven Josephson junctions, the
dc transport of the devices is analysed. The critical current as a function of temperature
is measured and it is possible to determine the induced superconducting gap. Under
rf illumination Shapiro steps form in the current voltage characteristic. A missing first
step at low frequencies and low powers is found in our devices. This is a signature of
a 4π-periodic supercurrent. By studying the device in a wide parameter range - as a
147148 SUMMARY
function of frequency, power, device geometry and magnetic field - it is shown that the
results are in agreement with the presence of a single gapless Andreev doublet and several
conventional modes.
Chapter 4 gives results of the numerical modelling of the I −V dynamics in a Josephson
junction where both a 2π- and a 4π-periodic supercurrents are present. This is done in
the framework of an equivalent circuit representation, namely the resistively shunted
Josephson junction model (RSJ-model). The numerical modelling is in agreement with
the experimental results in chapter 3. First, the missing of odd Shapiro steps can be
understood by a small 4π-periodic supercurrent contribution and a large number of
modes which have a conventional 2π-periodicity. Second, the missing of odd Shapiro
steps occurs at low frequency and low rf power. Third, it is shown that stochastic processes
like Landau Zener tunnelling are most probably not responsible for the 4π contribution.
In a next step the periodicity of Josephson junctions based on quantum spin Hall
insulators using are investigated in chapter 5. A fabrication process of Josephson junctions
based on inverted HgTe quantum wells was successfully developed. In order to achieve a
good proximity effect the barrier material was removed and the superconductor deposited
without exposing the structure to air. In a next step a gate electrode was fabricated which
allows the chemical potential of the quantum well to be tuned. The measurement of the
diffraction pattern of the critical current Ic due to a magnetic field applied perpendicular
to the sample plane was conducted. In the vicinity to the expected quantum spin Hall
phase, the pattern resembles that of a superconducting quantum interference device
(SQUID). This shows that the current flows predominantly on the edges of the mesa.
This observation is taken as a proof of the presence of edge currents. By irradiating the
sample with rf, missing odd Shapiro steps up to step index n = 9 have been observed. This
evidences the presence of a 4π-periodic contribution to the supercurrent. The experiment
is repeated using a weak link based on a non-inverted HgTe quantum well. This material
is expected to be a normal band insulator without helical edge channels. In this device,
all the expected Shapiro steps are observed even at low frequencies and over the whole
gate voltage range. This shows that the observed phenomena are directly connected
to the topological band structure. Both features, namely the missing of odd Shapiro
steps and the SQUID like diffraction pattern, appear strongest towards the quantum spin
Hall regime, and thus provide evidence for induced topological superconductivity in the
helical edge states.
A more direct way to probe the periodicity of the Josephson supercurrent than using
Shapiro steps is the measurement of the emitted radiation of a weak link. This experiment
is presented in chapter 6. A conventional Josephson junction converts a dc bias V to
an ac current with a characteristic Josephson frequency fJ
= eV /h. In a topological
Josephson junction a frequency at half the Josephson frequency fJ /2 is expected. A
new measurement setup was developed in order to measure the emitted spectrum of a
single Josephson junction. With this setup the spectrum of a HgTe quantum well based
Josephson junction was measured and the emission at half the Josephson frequency fJ /2
was detected. In addition, fJ emission is also detected depending on the gate voltage and
detection frequency. The spectrum is again dominated by half the Josephson emission at
low voltages while the conventional emission is determines the spectrum at high voltages.
A non-inverted quantum well shows only conventional emission over the whole gateSUMMARY 149
voltage and frequency range. The linewidth of the detected frequencies gives a measure
on the lifetime of the bound states: From there, a coherence time of 0.3–4ns for the fJ /2
line has been deduced. This is generally shorter than for the fJ line (3–4ns).
The last part of the thesis, chapter 7, reports on the induced superconducting state
in a strained HgTe layer investigated by point-contact Andreev reflection spectroscopy.
For the experiment, a HgTe mesa was fabricated with a small constriction. The diameter
of the orifice was chosen to be smaller than the mean free path estimated from magne-
totransport measurements. Thus one gets a ballistic point-contact which allows energy
resolved spectroscopy. One part of the mesa is covered with a superconductor which
induces superconducting correlations into the surface states of the topological insulator.
This experiment therefore probes a single superconductor normal interface. In contrast to
the Josephson junctions studied previously, the geometry allows the acquisition of energy
resolved information of the induced superconducting state through the measurement
of the differential conductance dI/dV as a function of applied dc bias for various gate
voltages, temperatures and magnetic fields. An induced superconducting order parame-
ter of about 70µeV was extracted but also signatures of the niobium gap at the expected
value around Δ Nb
≈ 1.1meV have been found. Simulations using the theory developed by
Blonder, Tinkham and Klapwijk and an extended model taking the topological surface
states into account were used to fit the data. The simulations are in agreement with a
small barrier at the topological insulator-induced topological superconductor interface
and a high barrier at the Nb to topological insulator interface. To understand the full con-
ductance curve as a function of applied voltage, a non-equilibrium driven transformation
is suggested. The induced superconductivity is suppressed at a certain bias value due to
local electron population. In accordance with this suppression, the relevant scattering
regions change spatially as a function of applied bias.
To conclude, it is emphasized that the experiments conducted in this thesis found
clear signatures of induced topological superconductivity in HgTe based quantum well
and bulk devices and opens up the avenue to many experiments. It would be interesting
to apply the developed concepts to other topological matter-superconductor hybrid
systems. The direct spectroscopy and manipulation of the Andreev bound states using
circuit quantum electrodynamic techniques should be the next steps for HgTe based
samples. This was already achieved in superconducting atomic break junctions by the
group in Saclay [Science 2015, 349, 1199-1202 (2015)]. Another possible development
would be the on-chip detection of the emitted spectrum as a function of the phase φ
through the junction. In this connection, the topological junction needs to be shunted
by a parallel ancillary junction. Such a setup would allow the current phase relation
I(φ) directly and the lifetime of the bound states to be measured directly. By coupling
this system to a spectrometer, which can be another Josephson junction, the energy
dependence of the Andreev bound states E(φ) could be obtained. The experiments on
the Andreev reflection spectroscopy described in this thesis could easily be extended to
two dimensional topological insulators and to more complex geometries, like a phase
bias loop or a tunable barrier at the point-contact. This work might also be useful for
answering the question how and why Majorana bound states can be localized in quantum
spin Hall systems.
One of the most significant technological advances in history was driven by the utilization of a new material class: semiconductors.
Its most important application being the transistor, which is indispensable in our everyday life. The technological advance in the semiconductor industry, however, is about to slow down. Making transistors ever smaller to increase the performance and trying to reduce and deal with the dissipative heat will soon reach the limits dictated by quantum mechanics with Moore himself, predicting the death of his famous law in the next decade.
A possible successor for semiconductor transistors is the recently discovered material class of topological insulators. A material which in its bulk is insulating but has topological protected metallic surface states or edge states at its boundary. Their electrical transport characteristics include forbidden backscattering and spin-momentum-locking with the spin of the electron being perpendicular to its momentum. Topological insulators therefore offer an opportunity for high performance devices with low dissipation, and applications in spintronic where data is stored and processed at the same point.
The topological insulator Bi\(_2\)Se\(_3\) and related compounds offer relatively high energy band gaps and a rather simple band structure with a single dirac cone at the gamma point of the Brillouin zone. These characteritics make them ideal candidates to study the topological surface state in electrical transport experiments and explore its physics.
In this dissertation the electronic and high-energy optical properties of thin nanoscale
films of the magnetic topological insulator (MTI) (V,Cr)y(BixSb1-x)2-yTe3 are studied
by means of X-ray photoelectron spectroscopy (XPS) and electron energy-loss
spectroscopy (EELS). Magnetic topological insulators are presently of broad interest
as the combination of ferromagnetism and spin-orbit coupling in these materials
leads to a new topological phase, the quantum anomalous Hall state (QAHS), with
dissipation less conduction channels. Determining and controlling the physical
properties of these complex materials is therefore desirable for a fundamental understanding
of the QAHS and for their possible application in spintronics. EELS can
directly probe the electron energy-loss function of a material from which one can
obtain the complex dynamic dielectric function by means of the Kramers-Kronig
transformation and the Drude-Lindhard model of plasmon oscillations.
The XPS core-level spectra in (V,Cr)y(BixSb1-x)2-yTe3 are analyzed in detail with
regards to inelastic background contributions. It is shown that the spectra can be
accurately described based on the electron energy-loss function obtained from an
independent EELS measurement. This allows for a comprehensive and quantitative
analysis of the XPS data, which will facilitate future core-level spectroscopy studies
in this class of topological materials. From the EELS data, furthermore, the bulk and
surface optical properties were estimated, and compared to ab initio calculations
based on density functional theory (DFT) performed in the GW approximation
for Sb2Te3. The experimental results show a good agreement with the calculated
complex dielectric function and the calculated energy-loss function. The positions of
the main plasmon modes reported here are expected to be generally similar in other
materials in this class of nanoscale TI films. Hence, the present work introduces
EELS as a powerful method to access the high-energy optical properties of TI
thin films. Based on the presented results it will be interesting to explore more
systematically the effects of stoichiometry, magnetic doping, film thickness and
surface morphology on the electron-loss function, potentially leading to a better
understanding of the complex interplay of structural, electronic, magnetic and
optical properties in MTI nanostructures.
The presented thesis summarizes the results from four and a half years of intense lithography development on (Cd,Hg)Te/HgTe/(Cd,Hg)Te quantum well structures. The effort was motivated by the unique properties of this topological insulator. Previous work from Molenkamp at al.\ has proven that the transport through such a 2D TI is carried by electrons with opposite spin, counter-propagating in 1D channels along the sample edge. However, up to this thesis, the length of quantized spin Hall channels has never been reported to exceed 4 µm. Therefore, the main focus was put on a reproducible and easy-to-handle fabrication process that reveals the intrinsic material parameters.
Every single lithography step in macro as well as microscopic sample fabrication has been re-evaluated. In the Development, the process changes have been presented along SEM pictures, microgaphs and, whenever possible, measurement responses.
We have proven the conventional ion milling etch method to damage the remaining mesa and result in drastically lower electron mobilities in samples of microscopic size.
The novel KI:I2:HBr wet etch method for macro and microstructure mesa fabrication has been shown to leave the crystalline structure intact and result in unprecedented mobilities, as high as in macroscopic characterization Hall bars. Difficulties, such as an irregular etch start and slower etching of the conductive QW have been overcome by concentration, design and etch flow adaptations. In consideration of the diffusive regime, a frame around the EBL write field electrically decouples the structure mesa from the outside wafer. As the smallest structure, the frame is etched first and guarantees a non-different etching of the conductive layer during the redox reaction. A tube-pump method assures reproducible etch results with mesa heights below 300 nm. The PMMA etch mask is easy to strip and leaves a clean mesa with no redeposition. From the very first attempts, to the final etch process, the reader has been provided with the characteristics and design requirements necessary to enable the fabrication of nearly any mesa shape within an EBL write field of 200 µm.
Magneto resistance measurement of feed-back samples have been presented along the development chronology of wet etch method and subsequent lithography steps. With increasing feature quality, more and more physics has been revealed enabling detailed evaluation of smallest disturbances. The following lithography improvements have been implemented. They represent a tool-box for high quality macro and microstructure fabrication on (CdHg)Te/HgTe of almost any kind.
The optical positive resist ECI 3027 can be used as wet and as dry etch mask for structure sizes larger than 1 µm. It serves to etch mesa structures larger than the EBL write field.
The double layer PMMA is used for ohmic contact fabrication within the EBL write field. Its thickness allows to first dry etch the (Cd,Hg)Te cap layer and then evaporate the AuGe contact, in situ and self-aligned. Because of an undercut, up to 300 nm can be metalized without any sidewalls after the lift-off. An edge channel mismatch within the contact leads can be avoided, if the ohmic contacts are designed to reach close to the sample and beneath the later gate electrode.
The MIBK cleaning step prior to the gate application removes PMMA residuals and thereby improves gate and potential homogeneity.
The novel low HfO2-ALD process enables insulator growth into optical and EBL lift-off masks of any resolvable shape. Directly metalized after the insulator growth, the self-aligned method results in thin and homogeneous gate electrode reproducibly withholding gate voltages to +-10 V.
The optical negative resist ARN 4340 exhibits an undercut when developed. Usable as dry etch mask and lift-off resist, it enables an in-situ application of ohmic contacts first etching close to the QW, then metalizing AuGe. Up to 500 nm thickness, the undercut guarantees an a clean lift-off with no sidewalls.
The undertaken efforts have led to micro Hall bar measurements with Hall plateaus and SdH-oszillations in up to now unseen levels of detail.
The gap resistance of several micro Hall bars with a clear QSH signal have been presented in Quantum Spin Hall. The first to exhibit longitudinal resistances close to the expected h/2e2 since years, they reveal unprecedented details in features and characteristics. It has been shown that their protection against backscattering through time reversal symmetry is not as rigid as previously claimed. Values below and above 12.9 kΩ been explained, introducing backscattering within the Landauer-Büttiker formalism of edge channel transport. Possible reasons have been discussed. Kondo, interaction and Rashba-backscattering arising from density inhomogeneities close to the edge are most plausible to explain features on and deviations from a quantized value. Interaction, tunneling and dephasing mechanisms as well as puddle size, density of states and Rashba Fields are gate voltage dependent. Therefore, features in the QSH signal are fingerprints of the characteristic potential landscape.
Stable up to 11 K, two distinct but clear power laws have been found in the higher temperature dependence of the QSH in two samples. However, with ΔR = Tα, α = ¼ in one (QC0285) and α = 2 in the other (Q2745), none of the predicted dependencies could be confirmed. Whereas, the gap resistances of QC0285 remains QSH channel dominated up to 3.9 T and thereby confirmed the calculated lifting of the band inversion in magnetic field. The gate-dependent oscillating features in the QSH signal of Q2745 immediately increase in magnetic field. The distinct field dependencies allowed the assumption of two different dominant backscattering mechanisms.
Resulting in undisturbed magneto transport and unprecedented QSH measurements The Novel Micro Hall Bar Process has proven to enable the fabrication of a new generation of microstructures.
Topologische Isolatoren gehören zu einer Klasse von Materialien, an deren Realisation im Rahmen der zweiten quantenmechanischen Revolution gearbeitet wird. Einerseits sind zahlreiche Fragestellungen zu diesen Materialen und deren Nutzbarmachung noch nicht beantwortet, andererseits treiben vielversprechende Anwendungen im Feld der Quantencomputer und Spintronik die Lösung dieser Fragen voran. Topologische Rand- bzw. Oberflächenzustände wurden für unterschiedlichste Materialien und Strukturen theoretisch vorhergesagt, so auch für GaSb/InAs Doppelquantenfilme und Bi2Se3. Trotz intensiver Forschungsarbeiten und großer Fortschritte bedürfen viele Prozesse v. a. im Bereich der Probenherstellung und Verarbeitung noch der Optimierung. Die vorliegende Arbeit präsentiert Ergebnisse zur Molekularstahlepitaxie, zur Probenfertigung sowie zu elektro-optisch modulierter Transportuntersuchung von GaSb/InAs Doppelquantenfilmen und der epitaktischen Fertigung von Bi2Se3 Nanostrukturen.
Im ersten Teil dieser Arbeit werden die Parameter zur Molekularstrahlepitaxie sowie die Anpassung der Probenfertigung von GaSb/InAs Doppelquantenfilmen an material- und untersuchungsbedingte Notwendigkeiten beschrieben. Dieser verbesserte Prozess ermöglicht die Fertigung quantitativ vergleichbarer Probenserien. Anschließend werden Ergebnisse für Strukturen mit variabler InAs Schichtdicke unter elektrostatischer Kontrolle mit einem Frontgate präsentiert. Auch mit verbessertem Prozess zeigten sich Leckströme zum Substrat. Diese erschweren eine elektrostatische Kontrolle über Backgates. Die erstmals durch optische Anregung präsentierte Manipulation der Ladungsträgerart sowie des Phasenzustandes in GaSb/InAs Doppelquantenfilmen bietet eine Alternative zu problembehafteten elektrostatisch betriebenen Gates.
Im zweiten Teil wird die epitaktische Herstellung von Bi2Se3 Nanostrukturen gezeigt. Mit dem Ziel, Vorteile aus dem erhöhten Oberfläche-zu-Volumen Verhältnis zu ziehen, wurden im Rahmen dieser Arbeit erstmals Bi2Se3 Nanodrähte und -flocken mittels Molekularstrahlepitaxie für die Verwendung als topologischer Isolator hergestellt.
Ein Quantensprung – Kapitel 1 führt über die umgangssprachliche Wortbedeutung des Quantensprungs und des damit verbundenen Modells der Quantenmechanik in das Thema. Die Anwendung dieses Modells auf Quanten-Ensembles und dessen technische Realisation wird heute als erste Quantenmechanische Revolution bezeichnet und ist aus unserem Alltag nicht mehr wegzudenken. Im Rahmen der zweiten Quantenmechanischen Revolution soll nun die Anwendung auf einzelne Zustände realisiert und technisch nutzbar gemacht werden. Hierbei sind topologische Isolatoren ein vielversprechender Baustein. Es werden das Konzept des topologischen Isolators sowie die Eigenschaften der beiden in dieser Arbeit betrachteten Systeme beschrieben: GaSb/InAs Doppelquantenfilme und Bi2Se3 Nanostrukturen.
GaSb/InAs Doppelquantenfilme
Kapitel 2 beschreibt die notwendigen physikalischen und technischen Grundlagen. Ausgehend von der Entdeckung des Hall-Effekts 1879 werden die Quanten-Hall-Effekte eingeführt. Quanten-Spin-Hall-Isolatoren oder allgemeiner topologische Isolatoren sind Materialien mit einem isolierenden Inneren, weisen an der Oberfläche aber topologisch geschützte Zustände auf. Doppelquantenfilme aus GaSb/InAs, die in AlSb gebettet werden, weisen – abhängig vom Aufbau der Heterostruktur – eine typische invertierte Bandstruktur auf und sind ein vielversprechender Kandidat für die Nutzbarmachung der topologischen Isolatoren. GaSb, InAs und AlSb gehören zur 6,1 Ångström-Familie, welche für ihre opto-elektronischen Eigenschaften bekannt ist und häufig verwendet wird. Die Eigenschaften sowie die technologischen Grundlagen der epitaktischen Fertigung von Heterostrukturen aus den Materialien der 6,1 Ångström-Familie mittels Molekularstrahlepitaxie werden besprochen. Abschließend folgen die Charakterisierungs- und Messmethoden. Ein Überblick über die Literatur zu GaSb/InAs Doppelquantenfilmen in Bezug auf topologische Isolatoren rundet dieses Kapitel ab.
Zu Beginn dieser Arbeit stellten Kurzschlusskanäle eine Herausforderung für die Detektion der topologischen Randkanäle dar. Kapitel 3 behandelt Lösungsansätze hierfür und beschreibt die Verbesserung der Herstellung von GaSb/InAs Doppelquantenfilm-Strukturen mit Blick auf die zukünftige Realisation topologischer Randkanäle. In Abschnitt 3.1 werden numerische Simulationen präsentiert, die sich mit der Inversion der elektronischen Niveaus in Abhängigkeit der GaSb und InAs Schichtdicken dGaSb und dInAs beschäftigen. Ein geeigneter Schichtaufbau für Strukturen mit invertierter Bandordnung liegt im Parameterraum von 8 nm ≾ dInAs ≾ 12 nm und 8 nm ≾ dGaSb ≾ 10 nm. Abschnitt 3.2 beschreibt die epitaktische Herstellung von GaSb/InAs Doppelquantenfilmen mittels Molekularstrahlepitaxie. Die Fertigung eines GaSb Quasisubstrats auf ein GaAs Substrat wird präsentiert und anschließend der Wechsel auf native GaSb Substrate mit einer reduzierten Defektdichte sowie reproduzierbar hoher Probenqualität begründet. Ein Wechseln von binärem AlSb auf gitterangepasstes AlAsSb erlaubt die Verwendung dickerer Barrieren. Versuche, eine hinlängliche Isolation des Backgates durch das Einbringen einer dickeren unteren Barriere zu erreichen, werden in diesem Abschnitt diskutiert. In Abschnitt 3.3 wird die Optimierung der Probenprozessierung gezeigt. Die Kombination zweier angepasster Ätzprozesse – eines trockenchemischen und eines sukzessive folgenden nasschemischen Schrittes – liefert zusammen mit der Entfernung von Oberflächenoxiden reproduzierbar gute Ergebnisse. Ein materialselektiver Ätzprozess mit darauffolgender direkter Kontaktierung des InAs Quantenfilmes liefert gute Kontaktwiderstände, ohne Kurzschlusskanäle zu erzeugen. Abschnitt 3.4 gibt einen kompakten Überblick, über den im weiteren Verlauf der Arbeit verwendeten „best practice“ Prozess.
Mit diesem verbesserten Prozess wurden Proben mit variabler InAs Schichtdicke gefertigt und bei 4,2 K auf ihre Transporteigenschaften hin untersucht. Dies ist in Kapitel 4 präsentiert und diskutiert. Abschnitt 4.1 beschreibt die Serie aus drei Proben mit GaSb/InAs Doppelquantenfilm in AlSb Matrix mit einer variablen InAs Schichtdicke. Die InAs Schichtdicke wurde über numerische Simulationen so gewählt, dass je eine Probe im trivialen Regime, eine im invertierten Regime und eine am Übergang liegt. Gezeigt werden in Kapitel 4.2 Magnetotransportmessungen für konstante Frontgatespannungen sowie Messungen mit konstantem Magnetfeld gegen die Frontgatespannung. Die Messungen bestätigen eine Fertigung quantitativ vergleichbarer Proben, zeigen aber auch, dass keine der Proben im topologischen Regime liegt. Hierfür kommen mehrere Ursachen in Betracht: Eine Überschätzung der Hybridisierung durch die numerische Simulation, zu geringe InAs Schichtdicken in der Fertigung oder ein asymmetrisches Verschieben mit nur einem Gate (Kapitel 4.3). Zur Reduktion der Volumenleitfähigkeit wurden Al-haltigen Schichten am GaSb/InAs Übergang eingebracht. Die erwartete Widerstandssteigerung konnte in ersten Versuchen nicht gezeigt werde.
Die in Kapitel 5 gezeigte optische Manipulation des dominanten Ladungsträgertyps der InAs/GaSb-Doppelquantentöpfe gibt eine zusätzliche Kontrollmöglichkeit im Phasendiagramm. Optische Anregung ermöglicht den Wechsel der Majoritätsladungsträger von Elektronen zu Löchern. Dabei wird ein Regime durchlaufen, in dem beide Ladungsträger koexistieren. Dies weist stark auf eine Elektron-Loch-Hybridisierung mit nichttrivialer topologischer Phase hin. Dabei spielen zwei unterschiedliche physikalische Prozesse eine Rolle, die analog eines Frontgates bzw. eines Backgates wirken. Der Frontgate Effekt beruht auf der negativ persistenten Photoleitfähigkeit, der Backgate Effekt fußt auf der Akkumulation von Elektronen auf der Substratseite. Das hier gezeigte optisch kontrollierte Verschieben der Zustände belegt die Realisation von opto-elektronischem Schalten zwischen unterschiedlichen topologischen Phasen. Dies zeigt die Möglichkeit einer optischen Kontrolle des Phasendiagramms der topologischen Zustände in GaSb/InAs Doppelquantenfilmen. In Abschnitt 5.1 wird die optische Verstimmung von GaSb/InAs Quantenfilmen gezeigt und erklärt. Sie wird in Abhängigkeit von der Temperatur, der Anregungswellenlänge sowie der Anregungsintensität untersucht. Kontrollversuche an Proben mit einem unterschiedlichen Strukturaufbau zeigen, dass das Vorhandensein eines Übergitters auf der Substratseite der Quantenfilmstruktur essentiell für die Entstehung der Backgate-Wirkung ist (Abschnitt 5.2). Abschließend werden in Abschnitt 5.3 die Erkenntnisse zur optischen Kontrolle zusammengefasst und deren Möglichkeiten, wie optisch definierte topologischen Phasen-Grenzflächen, diskutiert.
Bi2Se3 Nanostrukturen
Mit Blick auf die Vorteile eines erhöhten Oberfläche-zu-Volumen Verhältnisses ist die Verwendung von Nanostrukturen für das Anwendungsgebiet der dreidimensionalen topologischen Isolatoren effizient. Mit dem Ziel, diesen Effekt für die Realisation des topologischen Isolators in Bi2Se3 auszunutzen, wurde im Rahmen dieser Arbeit erstmalig das Wachstum von Bi2Se3 Nanodrähten und -flocken mit Molekularstrahlepitaxie realisiert. In Kapitel 6 werden technische und physikalische Grundlagen hierzu erläutert (Abschnitt 6.1). Ausgehend von einer Einführung in dreidimensionale topologische Isolatoren werden die Eigenschaften des topologischen Zustandes in Bi2Se3 gezeigt. Darauf folgen die Kristalleigenschaften von Bi2Se3 sowie die Erklärung des epitaktischen Wachstums von Nanostrukturen mit Molekularstrahlepitaxie. In Abschnitt 6.2 schließt sich die Beschreibung der epitaktischen Herstellung an. Die Kristallstruktur wurde mittels hochauflösender Röntgendiffraktometrie und Transmissionselektronenmikroskopie als Bi2Se3 identifiziert. Rasterelektronenmikroskopie-Aufnahmen zeigen Nanodrähte und Nanoflocken auf mit Gold vorbehandelten bzw. nicht mit Gold vorbehandelten Proben. Der Wachstumsmechanismus für Nanodrähte kann nicht zweifelsfrei definiert werden. Das Fehlen von Goldtröpfchen an der Drahtspitze legt einen wurzelbasierten Wachstumsmechanismus nahe (Abschnitt 6.3).
Quantencomputer können manche Probleme deutlich effizienter lösen als klassische Rechner. Bisherige Umsetzungen leiden jedoch an einer zu geringen Dekohärenzzeit, weshalb die Lebenszeit der Quantenzustände einen limitierenden Faktor darstellt. Topologisch geschützte Anregungen, wie Majorana-Fermionen, könnten hingegen dieses Hindernis überwinden. Diese lassen sich beispielsweise in topologischen Supraleitern realisieren. Bis zum jetzigen Zeitpunkt existieren nur wenige Materialien, die dieses Phänomen aufweisen. Daher ist das Verständnis der elektronischen Eigenschaften für solche Verbindungen von großer Bedeutung.
In dieser Dissertation wird die Koexistenz von Supraleitung an der Probenoberfläche und topologischem Oberflächenzustand (engl. topological surface state, TSS) auf potentiellen topologischen Supraleitern überprüft. Diese beiden Bedingungen sind essentiell zur Ausbildung von topologischer Supraleitung in zeitumkehrgeschützten Systemen. Hierzu wird mittels Landaulevelspektroskopie und Quasiteilcheninterferenz das Vorhandensein des TSS am Ferminiveau auf Tl$_{x}$Bi$_{2}$Te$_{3}$ und Nb$_{x}$Bi$_{2}$Se$_{3}$ verifiziert, die mittels Transportmessungen als supraleitend identifiziert wurden. Anschließend folgen hochaufgelöste Spektroskopien an der Fermienergie, um die supraleitenden Eigenschaften zu analysieren.
Zur Interpretation der analysierten Eigenschaften wird zu Beginn der Ni-haltige Schwere-Fermion-Supraleiter TlNi$_{2}$Se$_{2}$ untersucht, der eine vergleichbare Übergangstemperatur besitzt. Anhand diesem werden die gängigen Messmethoden der Rastertunnelmikroskopie und -spektroskopie für supraleitende Proben vorgestellt und die Leistungsfähigkeit der Messapparatur demonstriert. Im Einklang mit der Literatur zeigt sich ein $s$-Wellencharakter des Paarungsmechanismus sowie die Formation eines für Typ~II-Supraleiter typischen Abrikosov-Gitters in schwachen externen Magnetfeldern.
Im folgenden Teil werden die potentiellen topologischen Supraleiter Tl$_{x}$Bi$_{2}$Te$_{3}$ und Nb$_{x}$Bi$_{2}$Se$_{3}$ begutachtet, für die eindeutig ein TSS bestätigt wird. Allerdings weisen beide Materialien keine Oberflächensupraleitung auf, was vermutlich durch eine Entkopplung der Oberfläche vom Volumen durch Bandverbiegung zu erklären ist. Unbeabsichtigte Kollisionen der Spitze mit der Probe führen jedoch zu supraleitenden Spitzen, die wesentlich erhöhte Werte für die kritische Temperatur und das kritische Feld zeigen.
Der letzte Abschnitt widmet sich dem supraleitenden Substrat Nb(110), für den der Reinigungsprozess erläutert wird. Hierbei sind kurze Heizschritte bis nahe des Schmelzpunktes nötig, um die bei Umgebungsbedingungen entstehende Sauerstoffrekonstruktion effektiv zu entfernen. Des Weiteren werden die elektronischen Eigenschaften untersucht, die eine Oberflächenresonanz zum Vorschein bringen. Hochaufgelöste Messungen lassen eine durch die BCS-Theorie gut repräsentierte Struktur der supraleitenden Energielücke erkennen. Magnetfeldabhängige Experimente offenbaren zudem eine mit der Kristallstruktur vereinbare Anisotropie des Paarungspotentials. Mit diesen Erkenntnissen kann Nb(110) zukünftig als Ausgang für das Wachstum von topologischen Supraleitern herangezogen werden.
The subject of this thesis is the fabrication and characterization of magnetic topological
insulator layers of (V,Bi,Sb)\(_2\)Te\(_3\) exhibiting the quantum anomalous Hall
effect. A major task was the experimental realization of the quantum anomalous
Hall effect, which is only observed in layers with very specific structural,
electronic and magnetic properties. These properties and their influence on the
quantum anomalous Hall effect are analyzed in detail.
First, the optimal conditions for the growth of pure Bi\(_2\)Te\(_3\) and Sb\(_2\)Te\(_3\) crystal
layers and the resulting structural quality are studied. The crystalline quality of
Bi\(_2\)Te\(_3\) improves significantly at higher growth temperatures resulting in a small
mosaicity-tilt and reduced twinning defects. The optimal growth temperature is
determined as 260\(^{\circ}\)C, low enough to avoid desorption while maintaining a high
crystalline quality.
The crystalline quality of Sb\(_2\)Te\(_3\) is less dependent on the growth temperature.
Temperatures below 230\(^{\circ}\)C are necessary to avoid significant material desorption,
though. Especially for the nucleation on Si(111)-H, a low sticking coefficient is
observed preventing the coalescence of islands into a homogeneous layer.
The influence of the substrate type, miscut and annealing sequence on the growth
of Bi\(_2\)Te\(_3\) layers is investigated. The alignment of the layer changes depending on
the miscut angle and annealing sequence: Typically, layer planes align parallel to
the Si(111) planes. This can enhance the twin suppression due to transfer of the
stacking order from the substrate to the layer at step edges, but results in a step
bunched layer morphology. For specific substrate preparations, however, the layer
planes are observed to align parallel to the surface plane. This alignment avoids
displacement at the step edges, which would cause anti-phase domains. This results
in narrow Bragg peaks in XRD rocking curve scans due to long-range order in
the absence of anti-phase domains. Furthermore, the use of rough Fe:InP(111):B
substrates leads to a strong reduction of twinning defects and a significantly reduced
mosaicity-twist due to the smaller lattice mismatch.
Next, the magnetically doped mixed compound V\(_z\)(Bi\(_{1−x}\)Sb\(_x\))\(_{2−z}\)Te\(_3\) is studied in
order to realize the quantum anomalous Hall effect. The addition of V and Bi to
Sb\(_2\)Te\(_3\) leads to efficient nucleation on the Si(111)-H surface and a closed, homogeneous
layer. Magneto-transport measurements of layers reveal a finite anomalous
Hall resistivity significantly below the von Klitzing constant. The observation of
the quantum anomalous Hall effect requires the complete suppression of parasitic
bulklike conduction due to defect induced carriers. This can be achieved by optimizing
the thickness, composition and growth conditions of the layers.
The growth temperature is observed to strongly influence the structural quality.
Elevated temperatures result in bigger islands, improved crystallographic orientation
and reduced twinning. On the other hand, desorption of primarily Sb is
observed, affecting the thickness, composition and reproducibility of the layers.
At 190\(^{\circ}\)C, desorption is avoided enabling precise control of layer thickness and
composition of the quaternary compound while maintaining a high structural
quality.
It is especially important to optimize the Bi/Sb ratio in the (V,Bi,Sb)\(_2\)Te\(_3\) layers,
since by alloying n-type Bi\(_2\)Te\(_3\) and p-type Sb\(_2\)Te\(_3\) charge neutrality is achieved at
a specific mixing ratio. This is necessary to shift the Fermi level into the magnetic
exchange gap and fully suppress the bulk conduction. The Sb content x furthermore
influences the in-plane lattice constant a significantly. This is utilized to
accurately determine x even for thin films below 10 nm thickness required for the
quantum anomalous Hall effect. Furthermore, x strongly influences the surface
morphology: with increasing x the island size decreases and the RMS roughness
increases by up to a factor of 4 between x = 0 and x = 1.
A series of samples with x varied between 0.56-0.95 is grown, while carefully
maintaining a constant thickness of 9 nm and a doping concentration of 2 at.% V.
Magneto-transport measurements reveal the charge neutral point around x = 0.86
at 4.2 K. The maximum of the anomalous Hall resistivity of 0.44 h/e\(^2\) is observed
at x = 0.77 close to charge neutrality. Reducing the measurement temperature
to 50 mK significantly increases the anomalous Hall resistivity. Several samples
in a narrow range of x between 0.76-0.79 show the quantum anomalous Hall effect
with the Hall resistivity reaching the von Klitzing constant and a vanishing
longitudinal resistivity. Having realized the quantum anomalous Hall effect as the
first group in Europe, this breakthrough enabled us to study the electronic and
magnetic properties of the samples in close collaborations with other groups.
In collaboration with the Physikalisch-Technische Bundesanstalt high-precision
measurements were conducted with detailed error analysis yielding a relative de-
viation from the von Klitzing constant of (0.17 \(\pm\) 0.25) * 10\(^{−6}\). This is published
as the smallest, most precise value at that time, proving the high quality of the
provided samples. This result paves the way for the application of magnetic topological
insulators as zero-field resistance standards.
Non-local magneto-transport measurements were conducted at 15 mK in close
collaboration with the transport group in EP3. The results prove that transport
happens through chiral edge channels. The detailed analysis of small anomalies in
transport measurements reveals instabilities in the magnetic phase even at 15 mK.
Their time dependent nature indicates the presence of superparamagnetic contributions
in the nominally ferromagnetic phase.
Next, the influence of the capping layer and the substrate type on structural properties
and the impact on the quantum anomalous Hall effect is investigated. To
this end, a layer was grown on a semi-insulating Fe:InP(111)B substrate using the
previously optimized growth conditions. The crystalline quality is improved significantly
with the mosaicity twist reduced from 5.4\(^{\circ}\) to 1.0\(^{\circ}\). Furthermore, a layer
without protective capping layer was grown on Si and studied after providing sufficient
time for degradation. The uncapped layer on Si shows perfect quantization,
while the layer on InP deviates by about 5%. This may be caused by the higher
crystalline quality, but variations in e.g. Sb content cannot be ruled out as the
cause. Overall, the quantum anomalous Hall effect seems robust against changes
in substrate and capping layer with only little deviations.
Furthermore, the dependence of the quantum anomalous Hall effect on the thickness
of the layers is investigated. Between 5-8 nm thickness the material typically
transitions from a 2D topological insulator with hybridized top and bottom surface
states to a 3D topological insulator. A set of samples with 6 nm, 8 nm, and
9 nm thickness exhibits the quantum anomalous Hall effect, while 5 nm and 15 nm
thick layers show significant bulk contributions. The analysis of the longitudinal
and Hall conductivity during the reversal of magnetization reveals distinct differences
between different thicknesses. The 6 nm thick layer shows scaling consistent
with the integer quantum Hall effect, while the 9 nm thick layer shows scaling expected
for the topological surface states of a 3D topological insulator. The unique
scaling of the 9 nm thick layer is of particular interest as it may be a result of
axion electrodynamics in a 3D topological insulator.
Subsequently, the influence of V doping on the structural and magnetic properties
of the host material is studied systematically. Similarly to Bi alloying, increased
V doping seems to flatten the layer surface significantly. With increasing V content,
Te bonding partners are observed to increase simultaneously in a 2:3 ratio
as expected for V incorporation on group-V sites. The linear contraction of the
in-plane and out-of-plane lattice constants with increasing V doping is quantitatively
consistent with the incorporation of V\(^{3+}\) ions, possibly mixed with V\(^{4+}\)
ions, at the group-V sites. This is consistent with SQUID measurements showing
a magnetization of 1.3 \(\mu_B\) per V ion.
Finally, magnetically doped topological insulator heterostructures are fabricated
and studied in magneto-transport. Trilayer heterostructures with a non-magnetic
(Bi,Sb)\(_2\)Te\(_3\) layer sandwiched between two magnetically doped layers are predicted
to host the axion insulator state if the two magnetic layers are decoupled and in
antiparallel configuration. Magneto-transport measurements of such a trilayer heterostructure
with 7 nm undoped (Bi,Sb)\(_2\)Te\(_3\) between 2 nm thick layers doped with
1.5 at.% V exhibit a zero Hall plateau representing an insulating state. Similar results
in the literature were interpreted as axion insulator state, but in the absence
of a measurement showing the antiparallel magnetic orientation other explanations
for the insulating state cannot be ruled out.
Furthermore, heterostructures including a 2 nm thin, highly V doped layer region
show an anomalous Hall effect of opposite sign compared to previous samples. A
dependency on the thickness and position of the doped layer region is observed,
which indicates that scattering at the interfaces causes contributions to the anomalous
Hall effect of opposite sign compared to bulk scattering effects.
Many interesting phenomena in quantum anomalous Hall insulators as well as axion
insulators are still not unambiguously observed. This includes Majorana bound
states in quantum anomalous Hall insulator/superconductor hybrid systems and
the topological magneto-electric effect in axion insulators. The limited observation
temperature of the quantum anomalous Hall effect of below 1 K could be increased
in 3D topological insulator/magnetic insulator heterostructures which utilize the
magnetic proximity effect.
The main achievement of this thesis is the reproducible growth and characterization
of (V,Bi,Sb)2Te3 layers exhibiting the quantum anomalous Hall effect. The
detailed study of the structural requirements of the quantum anomalous Hall effect
and the observation of the unique axionic scaling behavior in 3D magnetic
topological insulator layers leads to a better understanding of the nature of this
new quantum state. The high-precision measurements of the quantum anomalous
Hall effect reporting the smallest deviation from the von Klitzing constant
are an important step towards the realization of a zero-field quantum resistance
standard.
Spin-Orbit Torques and Galvanomagnetic Effects Generated by the 3D Topological Insulator HgTe
(2021)
Nature shows us only the tail of the lion. But I have no doubt that the lion belongs with it even if he cannot reveal himself all at once. Albert Einstein
In my dissertation, I addressed the question of whether the 3D topological insulator mercury telluride (3D TI HgTe) is a suitable material for spintronics applications. This question was addressed by investigating the SOTs generated by the 3D TI HgTe in an adjacent ferromagnet (Permalloy) by using the ferromagnetic resonance technique (SOT-FMR).
In the first part of the dissertation, the reader was introduced to the mathematical description of the SOTs of a hybrid system consisting of a topological insulator (TI) and a ferromagnet (FM). Furthermore, the sample preparation and the measurement setup for the SOT-FMR measurements were discussed. Our SOT-FMR measurements showed that at low temperatures (T = 4.2 K) the out-of-plane component of the torque is dominant. At room temperature, both in-plane and out-of-plane components of the torque could be observed. From the symmetry of the mixing voltage (Figs. 3.14 and 3.15) we could conclude that the 3D TI HgTe may be efficient for the generation of spin torques in the permalloy [1]. The investigations reported here showed that the SOT efficiencies generated by the 3D TI HgTe are comparable with other existent topological insulators (see Fig. 3.17). We also discussed in detail the parasitic effects (such as thermovoltages) that can contribute to the correct interpretation of the spin torque efficiencies.
Although the results reported here provide several indications that the 3D TI HgTe might be efficient in exerting spin-torques in adjacent ferromagnets [2], the reader was repeatedly made aware that parasitic effects might contaminate the correct writing and reading of the information in the ferromagnet. These effects should be taken into consideration when interpreting results in the published literature claiming high spin-orbit torque efficiencies [2–4]. The drawbacks of the SOT-FMR measurement method led to a further development of our measurement concept, in which the ferromagnet on top of the 3D TI HgTe was replaced by a
spin-valve structure. In contrast with our measurements, in this measurement setup, the current flowing through the HgTe is known and changes in the spin-valve resistance can be read via the GMR effect.
Moreover, the SOT-FMR experiments required the application of an in-plane magnetic field up to 300 mT to define the magnetization direction in the ferromagnet. Motivated by this fact, we investigated the influence of an in-plane magnetic field in the magnetoresistance of the 3D TI HgTe. The surprising results of these measurements are described in the second part of the dissertation. Although the TI studied here is non-magnetic, its transversal MR (Rxy) showed an oscillating behavior that depended on the angle between the in-plane magnetic field and the electrical current. This effect is a typical property of ferromagnetic materials and is called planar Hall effect (PHE) [5, 6]. Moreover, it was also shown that the PHE amplitude (Rxy) and the longitudinal resistance (Rxx) oscillate as a function of the in-plane magnetic field amplitude for a wide range of carrier densities of the topological insulator.
The PHE was already described in another TI material (Bi2−xSbxTe3) [7]. The authors suggested as a possible mechanism the scattering of the electron off impurities that are polarized by an in-plane magnetic field. We critically discussed this and other theoretical proposed mechanisms existent in the literature [8, 9].
In this thesis, we attempted to explain the origin of the PHE in the 3D TI HgTe by anisotropies in the band structure of this material. The k.p calculations based on 6-orbitals were able to demonstrate that an interplay between Rashba, Dresselhaus, and in-plane magnetic field deforms the Fermi contours of the camel back band of the 3D TI HgTe, which could lead to anisotropies in its conductivity. However, the magnetic fields needed to experimentally observe this effect are as
high as 40 T, i.e., one order of magnitude higher than reported in our experiments. Additionally, calculations of the DoS to assess if there is a difference in the states for Bin parallel and Bin perpendicular to the current were, so far, inconclusive. Moreover, the complicated dependence of Rashba in the p-conducting
regime of HgTe [10] makes it not straightforward the inclusion of this term in the band structure calculations.
Despite the extensive efforts to understand the origin of the galvanomagnetic effects in the 3D TI HgTe, we could not determine a clear mechanism for the origin of the PHE and the MR oscillations studied in this thesis. However, our work clarifies and excludes a few mechanisms reported in the literature as the origin of these effects in the 3D TI HgTe. The major challenge, which still needs to be overcome, is to find a model that simultaneously explains the PHE, the gate dependence, and the oscillations in the magnetoresistance of the 3D TI HgTe as a function of the in-plane magnetic field.
To conclude, the author would like to express her hope to have brought the reader closer to the complexity of the questions addressed in this thesis and to have initiated them into the art of properly conducting electrical transport measurements on topological insulators with in-plane magnetic fields.
Neue physikalische Erkenntnisse vervollständigen die Sicht auf die Welt und erschließen gleichzeitig Wege für Folgeexperimente und technische Anwendungen. Das letzte Jahrzehnt der Festkörperforschung war vom zunehmenden Fokus der theoretischen und experimentellen Erkundung topologischer Materialien geprägt. Eine fundamentale Eigenschaft ist ihre Resistenz gegenüber solchen Störungen, welche spezielle physikalische Symmetrien nicht verletzen. Insbesondere die Topologischen Isolatoren - Halbleiter mit isolierenden Volumen- sowie gleichzeitig leitenden und spinpolarisierten Oberflächenzuständen - sind vielversprechende Kandidaten zur Realisierung breitgefächerter spintronischer Einsatzgebiete. Bis zur Verwirklichung von Quantencomputern und anderer, heute noch exotisch anmutender Konzepte bedarf es allerdings ein umfassenderes Verständnis der grundlegenden, physikalischen Zusammenhänge. Diese kommen vor allem an Grenzflächen zum Tragen, weshalb oberflächensensitive Methoden bei der Entdeckung der Topologischen Isolatoren eine wichtige Rolle spielten.
Im Rahmen dieser Arbeit werden daher strukturelle, elektronische und magnetische Eigenschaften Topologischer Isolatoren mittels Tieftemperatur-Rastertunnelmikroskopie und -spektroskopie sowie begleitenden Methoden untersucht.
Die Veränderung der Element-Ausgangskonzentration während dem Wachstum des prototypischen Topologischen Isolators Bi2Te3 führt zur Realisierung eines topologischen p-n Übergangs innerhalb des Kristalls. Bei einem spezifischen Verhältnis von Bi zu Te in der Schmelze kommt es aufgrund unterschiedlicher Erstarrungstemperaturen der Komponenten zu einer Ansammlung von Bi- und Te-reichen Gegenden an den gegenüberliegenden Enden des Kristalls. In diesen bildet sich infolge des jeweiligen Elementüberschusses durch Kristallersetzungen und -fehlstellen eine Dotierung des Materials aus. Daraus resultiert die Existenz eines Übergangsbereiches, welcher durch Transportmessungen verifiziert werden kann. Mit der räumlich auflösenden Rastertunnelmikroskopie wird diese Gegend lokalisiert und strukturell sowie elektronisch untersucht. Innerhalb des Übergangsbereiches treten charakteristische Kristalldefekte beider Arten auf - eine Defektunterdrückung bleibt folglich aus. Dennoch ist dort der Beitrag der Defekte zum Stromtransport aufgrund ihres gegensätzlichen Dotiercharakters vernachlässigbar, sodass der topologische Oberflächenzustand die maßgeblichen physikalischen Eigenschaften bestimmt. Darüber hinaus tritt der Übergangsbereich in energetischen und räumlichen Größenordnungen auf, die Anwendungen bei Raumtemperatur denkbar machen.
Neben der Veränderung Topologischer Isolatoren durch den gezielten Einsatz intrinsischer Kristalldefekte bieten magnetische Störungen die Möglichkeit zur Prüfung des topologischen Oberflächenzustandes auf dessen Widerstandsfähigkeit sowie der gegenseitigen Wechselwirkungen. Die Zeitumkehrinvarianz ist ursächlich für den topologischen Schutz des Oberflächenzustandes, weshalb magnetische Oberflächen- und Volumendotierung diese Symmetrie brechen und zu neuartigem Verhalten führen kann.
Die Oberflächendotierung Topologischer Isolatoren kann zu einer starken Bandverbiegung und einer energetischen Verschiebung des Fermi-Niveaus führen. Bei einer wohldosierten Menge der Adatome auf p-dotiertem Bi2Te3 kommt die Fermi-Energie innerhalb der Volumenzustands-Bandlücke zum Liegen. Folglich wird bei Energien rund um das Fermi-Niveau lediglich der topologische Oberflächenzustand bevölkert, welcher eine Wechselwirkung zwischen den Adatomen vermitteln kann. Für Mn-Adatome kann Rückstreuung beobachtet werden, die aufgrund der Zeitumkehrinvarianz in undotierten Topologischen Isolatoren verboten ist. Die überraschenderweise starken und fokussierten Streuintensitäten über mesoskopische Distanzen hinweg resultieren aus der ferromagnetischen Kopplung nahegelegener Adsorbate, was durch theoretische Berechnungen und Röntgendichroismus-Untersuchungen bestätigt wird. Gleichwohl wird für die Proben ein superparamagnetisches Verhalten beobachtet.
Im Gegensatz dazu führt die ausreichende Volumendotierung von Sb2Te3 mit V-Atomen zu einem weitreichend ferromagnetischen Verhalten. Erstaunlicherweise kann trotz der weitläufig verbreiteten Theorie Zeitumkehrinvarianz-gebrochener Dirac-Zustände und der experimentellen Entdeckung des Anormalen Quanten-Hall-Effektes in ähnlichen Probensystemen keinerlei Anzeichen einer spektroskopischen Bandlücke beobachtet werden. Dies ist eine direkte Auswirkung der dualen Natur der magnetischen Adatome: Während sie einerseits eine magnetisch induzierte Bandlücke öffnen, besetzen sie diese durch Störstellenresonanzen wieder. Ihr stark lokaler Charakter kann durch die Aufnahme ihrer räumlichen Verteilung aufgezeichnet werden und führt zu einer Mobilitäts-Bandlücke, deren Indizien durch vergleichende Untersuchungen an undotiertem und dotiertem Sb2Te3 bestätigt werden.
Realization and Spectroscopy of the Quantum Spin Hall Insulator Bismuthene on Silicon Carbide
(2022)
Topological matter is one of the most vibrant research fields of contemporary solid state physics since the theoretical prediction of the quantum spin Hall effect in graphene in 2005. Quantum spin Hall insulators possess a vanishing bulk conductivity but symmetry-protected, helical edge states that give rise to dissipationless charge transport.
The experimental verification of this exotic state of matter in 2007 lead to a boost of research activity in this field, inspired by possible ground-breaking future applications.
However, the use of the quantum spin Hall materials available to date is limited to cryogenic temperatures owing to their comparably small bulk band gaps.
In this thesis, we follow a novel approach to realize a quantum spin Hall material with a large energy gap and epitaxially grow bismuthene, i.e., Bi atoms adopting a honeycomb lattice, in a \((\sqrt{3}\times\sqrt{3})\) reconstruction on the semiconductor SiC(0001). In this way, we profit both from the honeycomb symmetry as well as the large spin-orbit coupling of Bi, which, in combination, give rise to a topologically non-trivial band gap on the order of one electronvolt.
An in-depth theoretical analysis demonstrates that the covalent bond between the Si and Bi atoms is not only stabilizing the Bi film but is pivotal to attain the quantum spin Hall phase.
The preparation of high-quality, unreconstructed SiC(0001) substrates sets the basis for the formation of bismuthene and requires an extensive procedure in ultra-pure dry H\(_2\) gas. Scanning tunneling microscopy measurements unveil the (\(1\times1\)) surface periodicity and smooth terrace planes, which are suitable for the growth of single Bi layers by means of molecular beam epitaxy. The chemical configuration of the resulting Bi film and its oxidation upon exposure to ambient atmosphere are inspected with X-ray photoelectron spectroscopy.
Angle-resolved photoelectron spectroscopy reveals the excellent agreement of probed and calculated band structure. In particular, it evidences a characteristic Rashba-splitting of the valence bands at the K point. Scanning tunneling spectroscopy probes signatures of this splitting, as well, and allows to determine the full band gap with a magnitude of \(E_\text{gap}\approx0.8\,\text{eV}\).
Constant-current images and local-density-of-state maps confirm the presence of a planar honeycomb lattice, which forms several domains due to different, yet equivalent, nucleation sites of the (\(\sqrt{3}\times\sqrt{3}\))-Bi reconstruction.
Differential conductivity measurements demonstrate that bismuthene edge states evolve at atomic steps of the SiC substrate. The probed, metallic local density of states is in agreement with the density of states expected from the edge state's energy dispersion found in density functional theory calculations - besides a pronounced dip at the Fermi level.
By means of temperature- and energy-dependent tunneling spectroscopy it is shown that the spectral properties of this suppressed density of states are successfully captured in the framework of the Tomonaga-Luttinger liquid theory and most likely originate from enhanced electronic correlations in the edge channel.
The motivation for this work has been contributing a step to the advancement of technology. A next leap in technology would be the realization of a scalable quantum computer. One potential route is via topological quantum computing. A profound understanding of topological materials is thus essential. My work contributes by the investigation of the exemplary topological material HgTe. The focus lies on the understanding of the topological surface states (TSS) and new possibilities to manipulate them appropriately. Traditionally top gate electrodes are used to adjust the carrier density in such semi-conductor materials. We found that the electric field of the top gate can further alter the properties of the HgTe layer. The formation of additional massive Volkov-Pankratov states limits the accessibility of the TSS. The understanding of these states and their interplay with the TSS is necessary to appropriately design devices and to ensure their desired properties. Similarly, I observed the existence and stability of TSSs even without a bandgap in the bulk band structure in the inversion induced Dirac semi-metal phase of compressively strained HgTe. The finding of topological surface states in inversion-induced Dirac semi-metals provides a consistent and simple explanation for the observation reported for \(\text{Cd}_3\text{As}_2\).
These observations have only been possible due to the high quality of the MBE grown HgTe layers and the access of different phases of HgTe via strain engineering. As a starting point I performed Magneto-transport measurements on 67 nm thick tensilely strained HgTe layers grown on a CdTe substrate. We observed multiple transport channels in this three-dimensional topological insulator and successfully identified them. Not only do the expected topological surface states exist, but also additional massive surface states have been observed. These additional massive surface states are formed due to the electrical field applied at the top gate, which is routinely used to vary the carrier density in the HgTe layer. The additional massive surface states are called Volkov-Pankratov states after B. A. Volkov and O. A. Pankratov. They predicted the existence of similar massive surface states at the interface of materials with mutually inverted bands. We first found indications for such massive Volkov-Pankratov states in high-frequency compressibility measurements for very high electron densities in a fruitful collaboration with LPA in Paris. Magneto-transport measurements and \(k \cdot p\) calculations revealed that such Volkov-Pankratov states are also responsible for the observed whole transport. We also found indications for similar massive VPS in the electron regime, which coexist with the topological surface states. The topological surface states exist over the full investigated gate range including a regime of pure topological insulator transport. To increase the variability of the topological surface states we introduced a modulation doping layer in the buffer layer. This modulation doping layer also enabled us to separate and identify the top and bottom topological surface states.
We used the variability of the bulk band structure of HgTe with strain to engineer the band structure of choice using virtual substrates. The virtual substrates enable us to grow compressively strained HgTe layers that do not possess a bandgap, but instead linear crossing points. These layers are predicted to beDirac semi-metals. Indeed I observed also topological surface states and massive Volkov-Pankratov states in the compressively strained Dirac semi-metal phase. The observation of topological surfaces states also in the Dirac semi-metal phase has two consequences: First, it highlights that no bulk bandgap is necessary to observe topological surface states. Second, the observation of TSS also in the Dirac semi-metal phase emphasizes the importance of the underlying band inversion in this phase. I could not find any clear signatures of the predicted disjoint topological surface states, which are typically called Fermi-arcs. The presence of topological surface states and massive Volkov-Pankratov states offer a simple explanation for the observed quantum Hall effect and other two-dimensional transport phenomena in the class of inversion induced Dirac semi-metals, as \(\text{Cd}_3\text{As}_2\). This emphasizes the importance of the inherent bulk band inversion of different topological materials and provides a consistent and elegant explanation for the observed phenomena in these materials. Additionally, it offers a route to design further experiments, devices, and thus the foundation for the induction of superconductivity and thus topological quantum computing.
Another possible path towards quantum computing has been proposed based on the chiral anomaly. The chiral anomaly is an apparent transport anomaly that manifests itself as an additional magnetic field-driven current in three-dimensional topological semimetals with a linear crossing point in their bulk band structure. I observed the chiral anomaly in compressively strained HgTe samples and performed multiple control experiments to identify the observed reduction of the magnetoresistance with the chiral anomaly. First, the dependence of the so-called negative magnetoresistance on the angle and strength of the magnetic field has been shown to fit the expectation for the chiral anomaly. Second, extrinsic effects as scattering could be excluded as a source for the observed negative MR using samples with different mobilities and thus impurity concentrations. Third, the necessity of the linear crossing point has been shown by shifting the electrochemical potential away from the linear crossing points, which diminished the negative magnetoresistance. Fourth, I could not observe a negative magnetoresistance in the three-dimensional topological insulator phase of HgTe. These observations together prove the existence of the chiral anomaly and verify compressively strained HgTe as Dirac semi-metal. Surprisingly, the chiral anomaly is also present in unstrained HgTe samples, which constitute a semi-metal with a quadratic band touching point. This observation reveals the relevance of the Zeeman effect for the chiral anomaly due to the lifting of the spin-degeneracy in these samples. Additionally to the chiral anomaly, the Dirac semi-metal phase of compressively strained HgTe showed other interesting effects. For low magnetic fields, a strong weak-antilocalization has been observed. Such a strong weak-anti-localization correction in a three-dimensional layer is surprising and interesting. Additionally, non-trivial magnetic field strength and direction dependencies have been observed. These include a strong positive magnetoresistance for high magnetic fields, which could indicate a metal-insulator transition. On a more device-oriented note, the semi-metal phase of unstrained HgTe constitutes the lower limit of the by strain engineering adjustable minimal carrier density of the topological surface states and thus of very high mobility.
To sum up, topological surface states have been observed in the three-dimensional topological insulator phase and the Dirac semi-metal phase of HgTe. The existence and accessibility of topological surface states are thus independent of the existence of a bandgap in the bulk band structure. The topological surface states can be accompanied by massive Volkov-Pankratov states. These VPS are created by electric fields, which are routinely applied to adjust the carrier density in semiconductor devices. The theoretical predicted chiral anomaly has been observed in the Dirac semi-metal phase of HgTe. In contrast to theoretical predictions, no indications for the Fermi-arc called disjoint surface states have been observed, but instead the topological and massive Volkov-Pankratov surface states have been found. These states are thus expected for all inversion-induced topological materials.
Quantum point contacts (QPCs) are one-dimensional constrictions in an otherwise extended two-dimensional electron or hole system. Since their first realization in GaAs based two-dimensional electron gases, QPCs have become basic building blocks of mesoscopic physics and are used in manifold experimental contexts. A so far unrealized goal however is the implementation of QPCs in the new material class of two-dimensional topological insulators, which host the emergence of the so-called quantum spin Hall (QSH) effect. The latter is characterized by the formation of conducting one-dimensional spin-polarized states at the device edges, while the bulk is insulating. Consequently, an implemented QPC technology can be utilized to bring the QSH edge channels in close spatial proximity, thus for example enabling the study of interaction effects between the edge states. The thesis at hand describes the technological realization as well as the subsequent experimental characterization and analysis of QPCs in a QSH system for the first time.
After an introduction is given in Chapter 1, the subsequent Chapter 2 starts with discussing the peculiar band structure of HgTe. The emergence of the QSH phase for HgTe quantum wells with an inverted band structure is explained. For the band inversion to occur, the quantum wells have to exhibit a well thickness d_QW above a critical value (d_QW > d_c = 6.3 nm). Subsequently, the concept of QPCs is explicated and the corresponding transport behaviour is analytically described. Following the discussion of relevant constraints when realizing a QPC technology in a QSH system, a newly developed lithography process utilizing a multi-step wet etching technique for fabricating QPC devices based on HgTe quantum wells is presented. Transport measurements of exemplary devices show the expected conductance quantization in steps of ΔG ≈ 2e^2/h within the conduction band for a topological as well as for a trivial (d_QW < d_c) QPC. For the topological case, the residual conductance within the bulk band gap saturates at G_QSH ≈ 2e^2/h due to presence of the QSH state, while it drops to G ≈ 0 for the trivial device. Moreover, bias voltage dependent measurements of the differential conductance of an inverted sample provide explicit proof of the unperturbed coexistence of topological and trivial transport modes.
In a next step, Chapter 3 describes the emergence of a QSH interferometer state in narrow QPC devices with a quantum well thickness of d_QW = 7 nm. Presented band structure calculations reveal that the spatial extension of the QSH edge states depends on the position of the Fermi energy within the bulk band gap. As a consequence, reservoir electrons with randomized spin couple to both edge channels with the same probability under certain conditions, thus causing the formation of a QSH ring. A straightforward model capturing and specifying the occurrence of such a QSH interferometer is provided as well as substantiated by two experimental plausibility checks. After relevant quantum phases are theoretically introduced, the discussion of the obtained data reveals the accumulation of an Aharonov-Bohm phase, of a dynamical Aharonov-Casher phase as well as of a spin-orbit Berry phase of π in appropriate QPC devices. These results are consistent with analytic model considerations.
The last part of this thesis, Chapter 4, covers the observation of an unexpected conductance pattern for QPC samples fabricated from quantum wells with d_QW = 10.5 nm. In these devices, an anomalous plateau at G ≈ e^2/h = 0.5 x G_QSH emerges in addition to the QSH phase entailed residual conductance of G_QSH ≈ 2e^2/h. This so-called 0.5 anomaly occurs only for a specific interval of QPC width values, while it starts to get lost for too large sample widths. Furthermore, presented temperature and bias voltage dependent measurements insinuate that the emergence of the 0.5 anomaly is related to a gapped topological state. Additional characterization of this peculiar transport regime is provided by the realization of a novel device concept, which integrates a QPC within a standard Hall bar geometry. The results of the experimental analysis of such a sample link the occurrence of the 0.5 anomaly to a backscattered QSH channel. Thus, following a single particle perspective argumentation, it is reasoned that only one edge channel is transmitted in the context of the 0.5 anomaly. Two theoretic models possibly explaining the emergence of the 0.5 anomaly -- based on electron-electron interactions -- are discussed.
To conclude, the implementation of a working QPC technology in a QSH system represents a paramount development in the context of researching two-dimensional topological insulators and enables a multitude of future experiments. QPC devices realized in a QSH system are for example envisaged to allow for the detection of Majorana fermions and parafermions. Furthermore, the reported formation of a QSH interferometer state in appropriate QPC devices is of high interest. The observed dynamical Aharonov-Casher phase in the QSH regime enables a controllable modulation of the topological conductance, thus providing the conceptual basis for a topological transistor. Moreover, due to the resilience of geometric phases against dephasing, the presence of a spin-orbit Berry phase of π represents a promising perspective with regard to possible quantum computation concepts. Besides that, the transmission of only one QSH edge channel due to the emergence of the 0.5 anomaly is equivalent to 100 % spin polarization, which is an essential ingredient for realizing spintronic applications. Hence, the thesis at hand covers the experimental detection of three effects of fundamental importance in the context of developing new generations of logic devices -- based on QPCs fabricated from topological HgTe quantum wells.
The subject of this thesis is the investigation of the transport properties of topological and massive surface states in the three-dimensional topological insulator Hg(Mn)Te. These surface states give rise to a variety of extraordinary transport phenomena, making this material system of great interest for research and technological applications. In this connection, many physical properties of the topological insulator Hg(Mn)Te still require in-depth exploration. The overall aim of this thesis is to analyze the quantum transport of HgTe-based devices ranging from hundreds of micrometers (macroscopic) down to a few micrometers in size (microscopic) in order to extend the overall understanding of surface states and the possibilities of their manipulation.
In order to exploit the full potential of our high-quality heterostructures, it was necessary to revise and improve the existing lithographic fabrication process of macroscopic three-dimensional Hg(Mn)Te samples. A novel lithographic standard recipe for the fabrication of the HgTe-based macrostructures was developed. This recipe includes the use of an optimized Hall bar design and wet etching instead of etching with high-energy \(\mathrm{{Ar^{+}}}\)-ions, which can damage the samples. Further, a hafnium oxide insulator is applied replacing the SiO\(_{2}\)/Si\(_{3}\)N\(_{4}\) dielectric in order to reduce thermal load. Moreover, the devices are metallized under an alternating angle to avoid discontinuities of the metal layers over the mesa edges. It was revealed that the application of gate-dielectric and top-gate metals results in n-type doping of the devices. This phenomenon could be attributed to quasi-free electrons tunneling from the trap states, which form at the interface cap layer/insulator, through the cap into the active layer. This finding led to the development of a new procedure to characterize wafer materials. It was found that the optimized lithographic processing steps do not unintentionally react chemically with our heterostructures, thus avoiding a degradation of the quality of the Hg(Mn)Te layer. The implementation of new contact structures Ti/Au, In/Ti/Au, and Al/Ti/Au did not result in any improvement compared to the standard structure AuGe/Au. However, a novel sample recipe could be developed, resulting in an intermixing of the contact metals (AuGe and Au) and fingering of metal into the mesa. The extent of the quality of the ohmic contacts obtained through this process has yet to be fully established.
This thesis further deals with the lithographic realization of three-dimensional HgTe-based microstructures measuring only a few micrometer in size. Thus, these structures are in the order of the mean free path and the spin relaxation length of topological surface state electrons. A lithographic process was developed enabling the fabrication of nearly any desired microscopic device structure. In this context, two techniques suitable for etching microscopic samples were realized, namely wet etching and the newly established inductively coupled plasma etching. While wet etching was found to preserve the crystal quality of the active layer best, inductively coupled plasma etching is characterized by high reproducibility and excellent structural fidelity. Hence, the etching technique employed depends on the envisaged type of experiment.
Magneto-transport measurements were carried out on the macroscopic HgTe-based devices fabricated by means of improved lithographic processing with respect to the transport properties of topological and massive surface states. It was revealed that due to the low charge carrier density present in the leads to the ohmic contacts, these regions can exhibit an insulating behavior at high magnetic fields and extremely low temperatures. As soon as the filling factor of the lowest Landau levels dropped below a critical value (\(\nu_{\mathrm{{c}}}\approx0.8\)), the conductance of the leads decreased significantly. It was demonstrated that the carrier density in the leads can be increased by the growth of modulation doping layers, a back-gate-electrode, light-emitting diode illumination, and by the application of an overlapping top-gate layout. This overlapping top-gate and a back-gate made it possible to manipulate the carrier density of the surface states on both sides of the Hg(Mn)Te layer independently. With this setup, it was identified that topological and massive surface states contribute to transport simultaneously in 3D Hg(Mn)Te. A model could be developed allowing the charge carrier systems populated in the sample to be determined unambiguously. Based on this model, the process of the re-entrant quantum Hall effect observed for the first time in three-dimensional topological insulators could be explained by an interplay of n-type topological and p-type massive surface states. A well-pronounced \(\nu=-1\rightarrow\nu=-2\rightarrow\nu=-1\) sequence of quantum Hall plateaus was found in manganese-doped HgTe-based samples. It is postulated that this is the condensed-matter realization of the parity anomaly in three-dimensional topological insulators. The actual nature of this phenomenon can be the subject of further research. In addition, the measurements have shown that inter-scattering occurs between counter-propagating quantum Hall edge states. The good quantization of the Hall conductance despite this inter-scattering indicates that only the unpaired edge states determine the transport properties of the system as a whole. The underlying inter-scattering mechanism is the topic of a publication in preparation.
Furthermore, three-dimensional HgTe-based microstructures shaped like the capital letter "H" were investigated regarding spin transport phenomena. The non-local voltage signals occurring in the measurements could be attributed to a current-induced spin polarization of the topological surface states due to electrons obeying spin-momentum locking. It was shown that the strength of this non-local signal is directly connected to the magnitude of the spin polarization and can be manipulated by the applied top-gate voltage. It was found that in these microstructures, the massive surface and bulk states, unlike the topological surface states, cannot contribute to this spin-associated phenomenon. On the contrary, it was demonstrated that the population of massive states results in a reduction of the spin polarization, either due to the possible inter-scattering of massive and topological surface states or due to the addition of an unpolarized electron background. The evidence of spin transport controllable by a top-gate-electrode makes the three-dimensional material system mercury telluride a promising candidate for further research in the field of spintronics.
This thesis focuses on investigating magneto-transport properties of a ferromagnetic topological insulator (V,Bi,Sb)2Te3. This material is most famously known for exhibiting the quantum anomalous Hall effect, a novel quantum state of matter that has opened up possibilities for potential applications in quantum metrology as a quantum standard of resistance, as well as for academic investigations into unusual magnetic properties and axion electrodynamics. All of those aspects are investigated in the thesis.
The thesis at hand is concerned with improving our understanding of and our control over transport properties of the three-dimensional topological insulator HgTe. Topological insulators are characterized by an insulating bulk and symmetry-protected metallic surface states. These topological surface states hold great promise for research and technology; at the same time, many properties of experimentally accessible topological insulator materials still need to be explored thoroughly. The overall aim of this thesis was to experimentally investigate micrometer-sized HgTe transport devices to observe the ballistic transport regime as well as intercarrier scattering and possibly identify special properties of the topological surface states.
Part I of the thesis presents lithographic developments concerned with etching small HgTe devices. The aim was to replace existing processes which relied on dry etching with high-energy \(\text{Ar}^+\) ions and an organic etch mask. This etching method is known to degrade the HgTe crystal quality. In addition, the etch mask turned out to be not durable for long etching processes and difficult to remove completely after etching. First, \(\text{BaF}_2\) was introduced as a new etch mask for dry etching to replace the organic etch mask. With common surface characterization techniques like SEM and XPS it was shown that \(\text{BaF}_2\) etch masks are easy to deposit, highly durable in common dry etching processes for \(\text{Hg}_{1-x}\text{Cd}_x\text{Te}\), and easy to remove in deionized water. Transport results of HgTe devices fabricated with the new etch mask are comparable to results obtained with the old process. At the same time, the new etch mask can withstand longer etching times and does not cause problems due to incomplete removal. Second, a new inductively coupled plasma dry etching process based on \(\text{CH}_4\) and Ar was introduced. This etching process is compatible with \(\text{BaF}_2\) etch masks and yields highly reproducible results. Transport results indicate that the new etching process does not degrade the crystal quality and is suitable to produce high-quality transport devices even in the micrometer range. A comparison with wet-etched samples shows that inductively coupled plasma etching introduces a pronounced edge roughness. This - usually undesirable - property is actually beneficial for some of the experiments in this study and mostly irrelevant for others. Therefore, most samples appearing in this thesis were fabricated with the new process.
Part II of the thesis details the advancements made in identifying topological and trivial states which contribute to transport in HgTe three-dimensional topological insulators. To this end, macroscopic Hall bar samples were fabricated from high-quality tensilely strained HgTe layers by means of the improved lithographic processes. All samples were equipped with a top gate electrode, and some also with a modulation doping layer or a back gate electrode to modify the carrier density of the surface states on both sides of the HgTe layer. Due to the high sample quality, Landau levels could be well-resolved in standard transport measurements down to magnetic fields of less than 0.5T. High-resolution measurements of the Landau level dispersion with gate voltage and magnetic field allowed disentangling different transport channels. The main result here is that the upper (electron) branches of the two topological surface states contribute to transport in all experimentally relevant density regimes, while the hole branch is not accessible. Far in n-regime bulk conduction band states give a minor contribution to transport. More importantly, trivial bulk valence band holes come into play close to the charge neutrality point. Further in p-regime, the strong applied gate voltage leads to the formation of two-dimensional, massive hole states at the HgTe surface. The interplay of different states gives rise to rich physics: Top gate-back gate maps revealed that an anticrossing of Landau levels from the two topological surface states occurs at equal filling. A possible explanation for this effect is a weak hybridization of the surface states; however, future studies need to further clarify this point. Furthermore, the superposition of n-type topological and p-type trivial surface states leads to an intriguing Landau level dispersion. The good quantization of the Hall conductance in this situation indicates that the counterpropagating edge states interact with each other. The nature of this interaction will be the topic of further research.
Part III of the thesis is focused on HgTe microstructures. These "channel samples" have a typical width of 0.5 to 4µm and a typical length of 5 to 80µm. The quality of these devices benefits particularly from the improved lithographic processes. As a result, the impurity mean free path of the topological surface state electrons is on the order of the device width and transport becomes semiballistic. This was verified by measuring the channel resistance in small magnetic fields in n-regime. The deflection of carriers towards the dissipative channel walls results in a pronounced peak in the magnetoresistance, which scales in a predictable manner with the channel width. To investigate transport effects due to mutual scattering of charge carriers, the differential resistance of channel samples was measured as a function of carrier temperature. Selective heating of the charge carriers - but not the lattice - was achieved by passing a heating current through the channel. Increasing the carrier temperature has two pronounced effects when the Fermi level is situated in proximity to the bulk valence band maximum where the density of states is large. First, when both topological surface state electrons and bulk holes are present, electron-hole scattering leads to a pronounced increase in resistance with increasing carrier temperature. Second, a thermally induced increase of the electron and hole carrier densities reduces the resistance again at higher temperatures. A model considering these two effects was developed, which can well reproduce the experimental results. Current heating experiments in zero-gap HgTe quantum wells and compressively strained HgTe layers are consistent with this model. These observations raise the question as to how electron-hole scattering may affect other transport properties of HgTe-based three-dimensional topological insulators, which is briefly discussed in the outlook.
Novel appraches to the molecular beam epitaxy of core-shell nanowires in the group II telluride material system were explored in this work. Significant advances in growth spurred the development of a flexible and reliable platform for a charge transport characterization of the topological insulator HgTe in a tubular nanowire geometry. The transport results presented provide an important basis for the design of future studies that strive for the experimental realization of topological charge transport in the quantum wire limit.
Two-dimensional (2D) topological insulators are a new class of materials with properties that are
promising for potential future applications in quantum computers. For example, stanene represents
a possible candidate for a topological insulator made of Sn atoms arranged in a hexagonal
lattice. However, it has a relatively fragile low-energy spectrum and sensitive topology. Therefore,
to experimentally realize stanene in the topologically non-trivial phase, a suitable substrate
that accommodates stanene without compromising these topological properties must be found.
A heterostructure consisting of a SiC substrate with a buffer layer of adsorbed group-III elements
constitutes a possible solution for this problem. In this work, 2D adatom systems of Al and In
were grown epitaxially on SiC(0001) and then investigated structurally and spectroscopically by
scanning tunneling microscopy (STM) and photoelectron spectroscopy.
Al films in the high coverage regime \( (\Theta_{ML}\approx2\) ML\( ) \) exhibit unusually large, triangular- and
rectangular-shaped surface unit cells. Here, the low-energy electron diffraction (LEED)
pattern is brought into accordance with the surface topography derived from STM. Another Al
reconstruction, the quasi-one-dimensional (1D) Al phase, exhibits a striped surface corrugation,
which could be the result of the strain imprinted by the overlayer-substrate lattice mismatch.
It is suggested that Al atoms in different surface areas can occupy hexagonal close-packed and
face-centered cubic lattice sites, respectively, which in turn lead to close-packed transition regions
forming the stripe-like corrugations. On the basis of the well-known herringbone reconstruction
from Au(111), a first structural model is proposed, which fits well to the structural data from
STM. Ultimately, however, thermal treatments of the sample could not generate lower coverage
phases, i.e. in particular, a buffer layer structure.
Strong metallic signatures are found for In high coverage films \( (\Theta_{ML}\approx3\) to \(2\) ML\() \) by
scanning tunneling spectroscopy (STS) and angle-resolved photoelectron spectroscopy (ARPES),
which form a \( (7\times7) \), \( (6\times4\sqrt{3}) \), and \( (4\sqrt{3}\times4\sqrt{3}) \) surface reconstruction. In all these In phases
electrons follow the nearly-free electron model. Similar to the Al films, thermal treatments could
not obtain the buffer layer system.
Surprisingly, in the course of this investigation a triangular In lattice featuring a \( (1\times1) \)
periodicity is observed to host massive Dirac-like bands at \( K/K^{\prime} \) in ARPES. Based on this
strong electronic similarity with graphene at the Brillouin zone boundary, this new structure is
referred to as \textit{indenene}. An extensive theoretical analysis uncovers the emergence of an electronic
honeycomb network based on triangularly arranged In \textit{p} orbitals. Due to strong atomic spin-orbit
coupling and a comparably small substrate-induced in-plane inversion symmetry breaking this
material system is rendered topologically non-trivial. In indenene, the topology is intimately
linked to a bulk observable, i.e., the energy-dependent charge accumulation sequence within the
surface unit cell, which is experimentally exploited in STS to confirm the non-trivial topological
character. The band gap at \( K/K^{\prime} \), a signature of massive Dirac fermions, is estimated by
ARPES to approximately 125 meV. Further investigations by X-ray standing wave, STM, and
LEED confirm the structural properties of indenene. Thus, this thesis presents the growth and
characterization of the novel quantum spin Hall insulator material indenene.
Topological phenomena known from solid state physics have been transferred to a variety of other classical and quantum systems. Due to the equivalence of the Hamiltonian matrix describing tight binding models and the grounded circuit Laplacian describing an electrical circuit we can investigate such phenomena in circuits. By implementing different Hermitian topological models general suggestions on designing those types of circuit are worked out with the aim of minimizing unwanted coupling effects and parasitic admittances in the circuit. Here the existence and the spatial profile of topological states as well as the band structure of the model can be determined.
Due to the complex nature of electric admittance the investigations can be directly expanded to systems with broken Hermiticity. The particular advantages of the experimental investigation of non-exclusively topological phenomena by means of electric circuits come to light in the realization of non-Hermitian and non-linear models. Here we find limitation of the Hermitian bulk-boundary correspondence principle, purely real eigenvalues in non-Hermitian PT-symmetrical systems and edge localization of all eigenstates in non-Hermitian and non-reciprocal systems, which in literature is termed the non-Hermitian skin effect.
When systems obeying non-linear equations are studied, the grounded circuit Laplacian based on the Fourier-transform cannot be applied anymore. By combination of the connectivity of a topological system together with non-linear van der Pol oscillators self-activated and self-sustained topological edge oscillations can be found. These robust high frequency sinusoidal edge oscillations differ significantly from low frequency relaxation oscillations, which can be found in the bulk of the system.
A plethora of novel material concepts are currently being investigated in the condensed matter research community. Some of them hold promise to shape our everyday world in a way that silicon-based semiconductor materials and the related development of semiconductor devices have done in the past. In this regard, the last decades have witnessed an explosion of studies concerned with so called ‘’quantum materials’’ with emerging novel functionalities. These could eventually lead to new generations of electronic and/or spintronic devices. One particular material class, the so called topological materials, play a central role. As far as their technological applicability is concerned, however, they are still facing outstanding challenges to date.
Predicted for the first time in 2005 and experimentally verified in 2007, two-dimensional topological insulators (2D TIs) (a.k.a. quantum spin Hall insulators) exhibit the outstanding property of hosting spin-polarized metallic states along the boundaries of the insulating 2D bulk material, which are protected from elastic single-particle backscattering and give rise to the quantum spin Hall effect (QSHE). Owing to these peculiar properties the QSHE holds promise for dissipationless charge and/or spin transport. However, also in today’s best 2D TIs the observation of the QSHE is still limited to cryogenic temperatures of maximum 100 K. Here, the discovery of bismuthene on SiC(0001) has marked a milestone towards a possible realization of the QSHE at or beyond room-temperature owing to the massively increased electronic bulk energy gap on the order of 1 eV. This thesis is devoted to and motivated by the goal of advancing its synthesis and to build a deeper understanding of its one-particle and two-particle electronic properties that goes beyond prior work.
Regarding the aspect of material synthesis, an improved growth procedure for bismuthene is elaborated that increases the domain size of the material considerably (by a factor of ≈ 3.2 - 6.5 compared to prior work). The improved film quality is an important step towards any future device application of bismuthene, but also facilitates all further basic studies of this material.
Moreover, the deposition of magnetic transition metals (Mn and Co) on bismuthene is investigated. Thereby, the formation of ordered magnetic Bi-Mn/Co alloys is realized, their structure is resolved with scanning tunneling microscopy (STM), and their pristine electronic properties are resolved with scanning tunneling spectroscopy (STS) and photoemission spectroscopy (PES). It is proposed that these ordered magnetic Bi-Mn/Co-alloys offer the potential to study the interplay between magnetism and topology in bismuthene in the future.
In this thesis, a wide variety of spectroscopic techniques are employed that aim to build an understanding of the single-particle, as well as two-particle level of description of bismuthene's electronic structure. The techniques involve STS and angle-resolved PES (ARPES) on the one hand, but also optical spectroscopy and time-resolved ARPES (trARPES), on the other hand. Moreover, these experiments are accompanied by advanced numerical modelling in form of GW and Bethe-Salpeter equation calculations provided by our theoretical colleagues. Notably, by merging many experimental and theoretical techniques, this work sets a benchmark for electronic structure investigations of 2D materials in general.
Based on the STS studies, electronic quasi-particle interferences in quasi-1D line defects in bismuthene that are reminiscent of Fabry-Pérot states are discovered. It is shown that they point to a hybridization of two pairs of helical boundary modes across the line defect, which is accompanied by a (partial) lifting of their topological protection against elastic single-particle backscattering.
Optical spectroscopy is used to reveal bismuthene's two-particle elecronic structure. Despite its monolayer thickness, a strong optical (two-particle) response due to enhanced electron-hole Coulomb interactions is observed. The presented combined experimental and theoretical approach (including GW and Bethe-Salpeter equation calculations) allows to conclude that two prominent optical transitions can be associated with excitonic transitions derived from the Rashba-split valence bands of bismuthene. On a broader scope this discovery might promote further experiments to elucidate links of excitonic and topological physics.
Finally, the excited conduction band states of bismuthene are mapped in energy and momentum space employing trARPES on bismuthene for the first time. The direct and indirect band gaps are succesfully extracted and the effect of excited charge carrier induced gap-renormalization is observed. In addition, an exceptionally fast excited charge carrier relaxation is identified which is explained by the presence of a quasi-metallic density of states from coupled topological boundary states of domain boundaries.
After the discovery of three-dimensional topological insulators (TIs), such as tetradymite chalcogenides Bi$_2$Se$_3$, Bi$_2$Te$_3$ and Sb$_2$Te$_3$ – a new class of quantum materials characterized by their unique surface electronic properties – the solid state community got focused on topological states that are driven by strong electronic correlations and magnetism. An important material class is the magnetic TI (MTI) exhibiting the quantum anomalous Hall (QAH) effect, i.e. a dissipationless quantized edge-state transport in the absence of external magnetic field, originating from the interplay between ferromagnetism and a topologically non-trivial band structure. The unprecedented opportunities offered by these new exotic materials open a new avenue for the development of low-dissipation electronics, spintronics, and quantum computation. However, the major concern with QAH effect is its extremely low onset temperature, limiting its practical application. To resolve this problem, a comprehensive understanding of the microscopic origin of the underlying ferromagnetism is necessary.
V- and Cr-doped (Bi,Sb)$_2$Te$_3$ are the two prototypical systems that have been widely studied as realizations of the QAH state. Finding microscopic differences between the strongly correlated V and Cr impurities would help finding a relevant model of ferromagnetic coupling and eventually provide better control of the QAH effect in these systems. Therefore, this thesis first focuses on the V- and Cr-doped (Bi,Sb)$_2$Te$_3$ systems, to better understand these differences. Exploiting the unique capabilities of x-ray absorption spectroscopy and magnetic circular dichroism (XAS/XMCD), combined with advanced modeling based on multiplet ligand-field theory (MLFT), we provide a detailed microscopic insight into the local electronic and magnetic properties of these systems and determine microscopic parameters crucial for the comparison with theoretical models, which include the $d$-shell filling, spin and orbital magnetic moments. We find a strongly covalent ground state, dominated by the superposition of one and two Te-ligand-hole configurations, with a negligible contribution from a purely ionic 3+ configuration. Our findings indicate the importance of the Te $5p$ states for the ferromagnetism in (Bi, Sb)$_2$Te$_3$ and favor magnetic coupling mechanisms involving $pd$-exchange. Using state-of-the-art density functional theory (DFT) calculations in combination with XMCD and resonant photoelectron spectroscopy (resPES), we reveal the important role of the $3d$ impurity states in mediating magnetic exchange coupling. Our calculations illustrate that the kind and strength of the exchange coupling varies with the impurity $3d$-shell occupation. We find a weakening of ferromagnetic properties upon the increase of doping concentration, as well as with the substitution of Bi at the Sb site. Finally, we qualitatively describe the origin of the induced magnetic moments at the Te and Sb sites in the host lattice and discuss their role in mediating a robust ferromagnetism based on a $pd$-exchange interaction scenario. Our findings reveal important clues to designing higher $T_{\text{C}}$ MTIs.
Rare-earth ions typically exhibit larger magnetic moments than transition-metal ions and thus promise the opening of a wider exchange gap in the Dirac surface states of TIs, which is favorable for the realization of the high-temperature QAH effect. Therefore, we have further focused on Eu-doped Bi$_2$Te$_3$ and scrutinized whether the conditions for formation of a substantial gap in this system are present by combining spectroscopic and bulk characterization methods with theoretical calculations. For all studied Eu doping concentrations, our atomic multiplet analysis of the $M_{4,5}$ x-ray absorption and magnetic circular dichroism spectra reveals a Eu$^{2+}$ valence, unlike most other rare earth elements, and confirms a large magnetic moment. At temperatures below 10 K, bulk magnetometry indicates the onset of antiferromagnetic ordering. This is in good agreement with DFT results, which predict AFM interactions between the Eu impurities due to the direct overlap of the impurity wave functions. Our results support the notion of antiferromagnetism coexisting with topological surface states in rare-earth doped Bi$_2$Te$_3$ and corroborate the potential of such doping to result in an antiferromagnetic TI with exotic quantum properties.
The doping with impurities introduces disorder detrimental for the QAH effect, which may be avoided in stoichiometric, well-ordered magnetic compounds. In the last part of the thesis we have investigated the recently discovered intrinsic magnetic TI (IMTI) MnBi$_6$Te$_{10}$, where we have uncovered robust ferromagnetism with $T_{\text{C}} \approx 12$ K and connected its origin to the Mn/Bi intermixing. Our measurements reveal a magnetically intact surface with a large moment, and with FM properties similar to the bulk, which makes MnBi$_6$Te$_{10}$ a promising candidate for the QAH effect at elevated temperatures. Moreover, using an advanced ab initio MLFT approach we have determined the ground-state properties of Mn and revealed a predominant contribution of the $d^5$ configuration to the ground state, resulting in a $d$-shell electron occupation $n_d = 5.31$ and a large magnetic moment, in excellent agreement with our DFT calculations and the bulk magnetometry data. Our results together with first principle calculations based on the DFT-GGA$+U$, performed by our collaborators, suggest that carefully engineered intermixing plays a crucial role in achieving a robust long-range FM order and therefore could be the key for achieving enhanced QAH effect properties.
We expect our findings to aid better understanding of MTIs, which is essential to help increasing the temperature of the QAH effect, thus facilitating the realization of low-power electronics in the future.
Einerseits besteht die einfachste Möglichkeit zum Ladungs- und Informationstransport zwischen zwei Punkten in deren direkter Verbindung durch eindimensionale Kanäle. Andererseits besitzen topologische Materialien exotische und äußerst vorteilhafte Eigenschaften, weshalb es nahe liegt, dass schon bald neue Anwendungen aus ihnen realisiert werden. Wenn diese beiden Entwicklungen zusammenkommen, dann ist ein grundlegendes Verständnis von Quanteninterferenz oder Hybridisierungseffekten in eindimensionalen, topologischen Kanälen von fundamentaler Wichtigkeit. Deshalb werden in der vorliegenden Arbeit Wechselwirkungen von eindimensionalen, topologisch geschützten Kantenzuständen, die an ungeradzahligen Stufenkanten auf der (001)–Oberfläche von Pb1−xSnxSe auftreten, untersucht. Aufgrund der lateralen Lokalisierung auf wenige Nanometer um eine Stufenkante herum und der Notwendigkeit zwischen gerad- und ungeradzahligen Stufenkantenhöhen zu unterscheiden, bieten sich die Rastertunnelmikroskopie und -spektroskopie als Methoden an. Die neu entdeckten Kopplungs- bzw. Wechselwirkungseffekte zwischen benachbarten Kantenzuständen treten auf, sobald der Stufe zu Stufe Abstand einen kritischen Wert von dkri ≈ 25nm unterschreitet. Dieses Kriterium kann durch verschiedene räumliche Anordnungen von Stufenkanten erfüllt werden. Infolgedessen werden sich kreuzende, parallel verlaufende und zusammenlaufende Stufenkanten genauer untersucht. Bei letzteren verändert sich entlang der Struktur kontinuierlich der Abstand und damit die Kopplungsstärke zwischen den beiden Randkanälen. Infolgedessen wurden drei Koppelungsregime identifiziert. (I) Ausgehend von einer schwachen Wechselwirkung zeigt der für die Kantenzustände charakteristische Peak im Spektrum zunächst eine Verbreiterung und Verminderung der Intensität. (II) Mit weiter zunehmender Wechselwirkung beginnt sich der Zustand in zwei Peaks aufzuspalten, sodass ab dkri ≈ 15nm an beiden Stufenkanten durchgehen eine Doppelpeak zu beobachten ist . Mit weiter abnehmendem Abstand erreicht die Aufspaltung Werte von einigen 10 meV, während sich die Intensität weiter reduziert. (III) Sobald zwei Stufenkanten weniger als etwa 5nm voneinander getrennt sind, konvergieren aufgrund der schwindenden Intensität und des sinkenden energetischen Abstands der beiden Peaks zu den van Hove Singularitäten die Spektren an den Stufenkanten gegen das Spektrum über einer Terrasse. i Die Aufspaltung verläuft in den Bereichen I und II asymmetrisch, d. h. ein Peak verbleibt ungefähr bei der Ausgangsenergie, während der andere mit zunehmender Kopplung immer weiter weg schiebt. Bezüglich der Asymmetrie kann kein Unterschied festgestellt werden, ob die zusammenlaufenden Stufenkanten eine Insel oder Fehlstelleninsel bilden oder ob die Stufenkanten sogar gänzlich parallel verlaufen. Es zeigt sich keine Präferenz, ob zunächst der niederenergetische oder der hochenergetische Peak schiebt. Erst im Regime starker Kopplung (III) kann beobachtet werden, dass beide Peaks die Ausgangsenergie deutlich verlassen. Im Gegensatz dazu kann bei sich kreuzenden Stufen ein erheblicher Einfluss der Geometrie, in Form des eingeschlossenen Winkels, auf das Spektrum beobachtet werden. Unabhängig vom Winkel existiert am Kreuzungspunkt selbst kein Kantenzustand mehr. Die Zustände an den vier Stufen beginnen, abhängig vom Winkel, etwa 10-15nm vor dem Kreuzungspunkt abzuklingen. Überraschenderweise zeigt sich dabei, dass im Fall rechtwinkliger Stufen gar keine Aufspaltung zu beobachten ist, während bei allen anderen Winkeln ein Doppelpeak festgestellt werden kann. Diese Entdeckung deutet auf Orthogonalität bezüglich einer Quantenzahl bei den beteiligten Kantenzustände hin. Neben einer nur theoretisch vorhergesagten Spinpolarisation kann dieser Effekt auch von dem orbitalem Charakter der beteiligten Dirac–Kegel verursacht sein. Da der topologische Schutz in Pb1−xSnxSe durch Kristallsymmetrien garantiert ist, wird als letzter intrinsischer Effekt der Einfluss von eindimensionalen Defekten auf die Kantenzustände untersucht. Berücksichtigt werden dabei ein nicht näher klassifizierbarer, oberflächennaher Defekt und Schraubversetzungen. In beiden Fällen kann ebenfalls eine Aufspaltung des Kantenzustands in einen Doppelpeak gezeigt werden. Im zweiten Teil dieser Arbeit werden die Grundlagen für eine Wiederverwendung von (Pb,Sn)Se–Oberflächen bei zukünftige Experimenten mit (magnetischen) Adatomen geschaffen. Durch Kombination von Inoenzerstäubung und Tempern wird dabei nicht nur eine gereinigte Oberfläche erzeugt, sondern es kann auch das Ferminiveau gezielt erhöht oder gesenkt werden. Dieser Effekt beruht auf eine Modifikation der Sn– Konzentration und der von ihr kontrollierten Anzahl an Defektelektronen. Als letztes sind erste Messungen an Cu- und Fe–dotierte Proben gezeigt. Durch die Adatome tritt eine n–Dotierung auf, welche den Dirac–Punkt des Systems in Richtung des Ferminiveaus verschiebt. Sobald er dieses erreicht hat kommt es zu Wechselwirkungsphänomenen an freistehenden Stufenkanten. Dies führt zu einer Doppelpeakstruktur mit einer feinen Aufspaltung von wenigen meV. Das Phänomen ist auf ein schmales Energiefenster beschränkt, bei dem die Lage des Dirac–Punkts nur etwa 5 meV (in beide Richtungen) von der des Ferminiveaus abweichen darf.
This thesis examines the electronic properties of two materials that promise the realization and observation of novel exotic quantum phenomena. For this purpose, angle-resolved photoemission forms the experimental basis for the investigation of the electronic properties. Furthermore, the magnetic order is investigated utilizing X-ray dichroism measurements.
First, the bulk and surface electronic structure of epitaxially grown HgTe in its three-dimensional topological insulator phase is investigated. In this study, synchrotron radiation is used to address the three-dimensional band structure and orbital composition of the bulk states by employing photon-energy-dependent and polarization-dependent measurements, respectively. In addition, the topological surface state is examined on in situ grown samples using a laboratory photon source. The resulting data provide a means to experimentally localize the bulk band inversion in momentum space and to evidence the momentum-dependent change in the orbital character of the inverted bulk states.
Furthermore, a rather new series of van der Waals compounds, (MnBi\(_2\)Te\(_4\))(Bi\(_2\)Te\(_3\))\(_n\), is investigated. First, the magnetic properties of the first two members of the series, MnBi\(_2\)Te\(_4\) and MnBi\(_4\)Te\(_7\), are studied via X-ray absorption-based techniques. The topological surface state on the two terminations of MnBi\(_4\)Te\(_7\) is analyzed using circular dichroic, photon-energy-dependent, and spin-resolved photoemission. The topological state on the (MnBi\(_2\)Te\(_4\))-layer termination shows a free-standing Dirac cone with its Dirac point located in the bulk band gap. In contrast, on the (Bi\(_2\)Te\(_3\))-layer termination the surface state hybridizes with the bulk valences states, forming a spectral weight gap, and exhibits a Dirac point that is buried within the bulk continuum. Lastly, the lack of unambiguous evidence in the literature showing a temperature-dependent mass gap opening in these magnetic topological insulators is discussed through MnBi\(_2\)Te\(_4\).
In this thesis, the Josephson effect in mercury telluride based superconducting quantum point contacts (SQPCs) is studied. Implementing such confined structures into topological superconductors has been proposed as a means to detect and braid Majorana fermions. For the successful realization of such experiments though, coherent transport across the constriction is essential. By demonstrating the Josephson effect in a confined topological system, the presented experiments lay the foundation for future quantum devices that can be used for quantum computation. In addition, the experiments also provide valuable insights into the behavior of the Josephson effect in the low-channel limit (N<20). Due to the confinement of the weak link, we can also study the Josephson effect in a topological insulator, where the edge modes interact.
In conclusion, this thesis discusses the fabrication of, and low-temperature measurements on mercury telluride quantum point contacts embedded within Josephson junctions. We find that the merging of the currently used fabrication methods for mercury telluride quantum point contacts and Josephson junctions does not yield a good enough device quality to resolve subbands of the quantum point contact as quantization effects in the transport properties. As we attribute this to the long dry etching time that is necessary for a top-contact, the fabrication process was adapted to reduce the defect density at the superconductor-semiconductor interface. Employing a technique that involves side contacting the mercury telluride quantum well and reducing the size of the mercury telluride mesa to sub-micrometer dimensions yields a quantized supercurrent across the junction. The observed supercurrent per mode is in good agreement with theoretical predictions for ballistic, one-dimensional modes that are longer than the Josephson penetration depth. Moreover, we find that oscillatory features superimpose the plateaus of the supercurrent and the conductance. The strength of these oscillatory features are sample-dependent and complicate the identification of plateaus. We suggest that the oscillatory features originate mainly from local defects and the short gate electrode. Additionally, resonances are promoted within the weak link if the transparency of the superconductor-HgTe interface differs from one.
Furthermore, the research explores the regimes of the quantum spin Hall effect and the 0.5 anomaly. Notably, a small yet finite supercurrent is detected in the QSH regime. In samples fabricated from thick mercury telluride quantum wells, the supercurrent appears to vanish when the quantum point contact is tuned into the regime of the 0.5 anomaly. For samples fabricated from thin mercury telluride quantum wells, the conductance as well as the supercurrent vanish for strong depopulation. In these samples though, the supercurrent remains detectable even for conductance values significantly below 2 e²/h.
Numerical calculation reproduce the transport behavior of the superconducting quantum point contacts.
Additionally, the topological nature of the weak link is thoroughly investigated using the supercurrent diffraction pattern and the absorption of radio frequency photons. The diffraction pattern reveals a gate independent, monotonous decay of $I_\text{sw}(B)$, which is associated with the quantum interference of Andreev bound states funneled through the quantum point contact. Interestingly, the current distribution in the weak link appears unaffected as the quantum point contact is depleted. In the RF measurements, indications of a 4π periodic supercurrent are observed as a suppression of odd Shapiro steps. The ratio of the 4π periodic current to the 2π periodic current appears to decrease for smaller supercurrents, as odd Shapiro steps are exclusively suppressed for large supercurrents. Additionally, considering the observation that the supercurrent is small when the bulk modes in the quantum point contact are fully depleted, we suggest that the re-emerging of odd Shapiro steps is a consequence of the group velocity of the edge modes being significantly suppressed when the bulk modes are absent. Consequently, the topological nature of the superconducting quantum point contact is only noticeable in the transport properties when bulk modes are transmitted through the superconducting quantum point contact.
The shown experiments are the first demonstration of mercury telluride superconducting quantum point contacts that exhibit signatures of quantization effects in the conductance as well as the supercurrent. Moreover, the experiments suggest that the regime of interacting topological edge channels is also accessible in mercury telluride superconducting quantum point contacts. This is potentially relevant for the realization of Majorana fermions and their application in the field of quantum computation.