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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.
The subject of this thesis is the growth of Hg\(_{1-x}\)Cd\(_2\)Te layers via molecular beam epitaxy (MBE).
This material system gives rise to a number of extraordinary physical phenomena related to its electronic band structure and therefore is of fundamental interest in research.
The main results can be divided into three main areas, the implementation of a temperature measurement system based on band edge thermometry (BET), improvements of CdTe virtual substrate growth and the investigation of Hg\(_{1-x}\)Cd\(_2\)Te for different compositions.
Magnetic particle imaging is an emerging tomographic method used for evaluation of the spatial distribution of iron‐oxide nanoparticles. In this work, the effect of the polymer coating on the response of particles was studied. Particles with covalently crosslinked coating showed improved signal and image resolution.
In order to facilitate the human energy needs with renewable energy sources in the future, new concepts and ideas for the electricity generation are needed. Solar cells based on metal halide perovskite semiconductors represent a promising approach to address these demands in both single-junction and tandem configurations with existing silicon technology. Despite intensive research, however, many physical properties and the working principle of perovskite PVs are still not fully understood. In particular, charge carrier recombination losses have so far mostly been studied on pure films not embedded in a complete solar cell. This thesis aimed for the identification and quantification of charge carrier recombination dynamics in fully working devices under conditions corresponding to those under real operation. To study different PV systems, transient electrical methods, more precisely Open-Circuit Voltage Decay (OCVD), Transient Photovoltage (TPV) and Charge Extraction (CE), were applied. Whereas OCVD and TPV provide information about the recombination lifetime, CE allows to access the charge carrier density at a specific illumination intensity. The benefit of combining these different methods is that the obtained quantities can not only be related to the Voc but also to each other, thus enabling to determine also the dominant recombination mechanisms.The aim of this thesis is to contribute to a better understanding of recombination losses in fully working perovskite solar cells and the experimental techniques which are applied to determine these losses.
In organic thin‐film transistors (TFTs) fabricated in the inverted (bottom‐gate) device structure, the surface roughness of the gate dielectric onto which the organic‐semiconductor layer is deposited is expected to have a significant effect on the TFT characteristics. To quantitatively evaluate this effect, a method to tune the surface roughness of a gate dielectric consisting of a thin layer of aluminum oxide and an alkylphosphonic acid self‐assembled monolayer over a wide range by controlling a single process parameter, namely the substrate temperature during the deposition of the aluminum gate electrodes, is developed. All other process parameters remain constant in the experiments, so that any differences observed in the TFT performance can be confidently ascribed to effects related to the difference in the gate‐dielectric surface roughness. It is found that an increase in surface roughness leads to a significant decrease in the effective charge‐carrier mobility and an increase in the subthreshold swing. It is shown that a larger gate‐dielectric surface roughness leads to a larger density of grain boundaries in the semiconductor layer, which in turn produces a larger density of localized trap states in the semiconductor.
Unlike the conventional p‐doping of organic semiconductors (OSCs) using acceptors, here, an efficient doping concept for diketopyrrolopyrrole‐based polymer PDPP[T]\(_{2}\)‐EDOT (OSC‐1) is presented using an oxidized p‐type semiconductor, Spiro‐OMeTAD(TFSI)\(_{2}\) (OSC‐2), exploiting electron transfer from HOMO\(_{OSC-1}\) to HOMO\(_{OSC-2}\). A shift of work function toward the HOMO\(_{OSC-1}\) upon doping is confirmed by ultraviolet photoelectron spectroscopy (UPS). Detailed X‐ray photoelectron spectroscopy (XPS) and UV–vis–NIR absorption studies confirm HOMO\(_{OSC-1}\) to HOMO\(_{OSC-2}\) electron transfer. The reduction products of Spiro‐OMeTAD(TFSI)\(_{2}\) to Spiro‐OMeTAD(TFSI) and Spiro‐OMeTAD is also confirmed and their relative amounts in doped samples is determined. Mott–Schottky analysis shows two orders of magnitude increase in free charge carrier density and one order of magnitude increase in the charge carrier mobility. The conductivity increases considerably by four orders of magnitude to a maximum of 10 S m\(^{-1}\) for a very low doping ratio of 8 mol%. The doped polymer films exhibit high thermal and ambient stability resulting in a maximum power factor of 0.07 µW m\(^{-1}\) K\(^{-2}\) at a Seebeck coefficient of 140 µV K\(^{-1}\) for a very low doping ratio of 4 mol%. Also, the concept of HOMO\(_{OSC-1}\) to HOMO\(_{OSC-2}\) electron transfer is a highly efficient, stable and generic way to p‐dope other conjugated polymers.
Spinning black holes in the centres of galaxies can release powerful magnetised jets. When the jets are observed at angles of less than a few degrees to the line-of-sight, they are called blazars, showing variable non-thermal emission across the electromagnetic spectrum from radio waves to gamma rays. It is commonly believed that shock waves are responsible for this dissipation of jet energy. Here we show that gamma-ray observations of the blazar 3C 279 with the space-borne telescope Fermi-LAT reveal a characteristic peak-in-peak variability pattern on time scales of minutes expected if the particle acceleration is instead due to relativistic magnetic reconnection. The absence of gamma-ray pair attenuation shows that particle acceleration takes place at a distance of ten thousand gravitational radii from the black hole where the fluid dynamical kink instability drives plasma turbulence.
This longitudinal study was performed to evaluate the feasibility of detecting the interaction between wall shear stress (WSS) and plaque development. 20 ApoE\(^{-/-}\)mice were separated in 12 mice with Western Diet and 8 mice with Chow Diet. Magnetic resonance (MR) scans at 17.6 Tesla and histological analysis were performed after one week, eight and twelve weeks. Allin vivoMR measurements were acquired using a flow sensitive phase contrast method for determining vectorial flow. Histological sections were stained with Hematoxylin and Eosin, Elastica van Gieson and CD68 staining. Data analysis was performed using Ensight and a Matlab-based "Flow Tool". The body weight of ApoE\(^{-/-}\)mice increased significantly over 12 weeks. WSS values increased in the Western Diet group over the time period; in contrast, in the Chow Diet group the values decreased from the first to the second measurement point. Western Diet mice showed small plaque formations with elastin fragmentations after 8 weeks and big plaque formations after 12 weeks; Chow Diet mice showed a few elastin fragmentations after 8 weeks and small plaque formations after 12 weeks. Favored by high-fat diet, plaque formation results in higher values of WSS. With wall shear stress being a known predictor for atherosclerotic plaque development, ultra highfield MRI can serve as a tool for studying the causes and beginnings of atherosclerosis.
A current challenge in condensed matter physics is the realization of strongly correlated, viscous electron fluids. These fluids can be described by holography, that is, by mapping them onto a weakly curved gravitational theory via gauge/gravity duality. The canonical system considered for realizations has been graphene. In this work, we show that Kagome systems with electron fillings adjusted to the Dirac nodes provide a much more compelling platform for realizations of viscous electron fluids, including non-linear effects such as turbulence. In particular, we find that in Scandium Herbertsmithite, the fine-structure constant, which measures the effective Coulomb interaction, is enhanced by a factor of about 3.2 as compared to graphene. We employ holography to estimate the ratio of the shear viscosity over the entropy density in Sc-Herbertsmithite, and find it about three times smaller than in graphene. These findings put the turbulent flow regime described by holography within the reach of experiments. Viscous electron fluids are predicted in strongly correlated systems but remain challenging to realize. Here, the authors predict enhanced effective Coulomb interaction and reduced ratio of the shear viscosity over entropy density in a Kagome metal, inferring turbulent flow of viscous electron fluids.
Elementary building blocks for quantum repeaters based on fiber channels and memory stations are analyzed. Implementations are considered for three different physical platforms, for which suitable components are available: quantum dots, trapped atoms and ions, and color centers in diamond. The performances of basic quantum repeater links for these platforms are evaluated and compared, both for present‐day, state‐of‐the‐art experimental parameters as well as for parameters that can in principle be reached in the future. The ultimate goal is to experimentally explore regimes at intermediate distances—up to a few 100 km—in which the repeater‐assisted secret key transmission rates exceed the maximal rate achievable via direct transmission. Two different protocols are considered, one of which is better adapted to the higher source clock rate and lower memory coherence time of the quantum dot platform, while the other circumvents the need of writing photonic quantum states into the memories in a heralded, nondestructive fashion. The elementary building blocks and protocols can be connected in a modular form to construct a quantum repeater system that is potentially scalable to large distances.