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- Topologischer Isolator (44) (entfernen)
The prediction and the experimental discovery of topological insulators has set the stage for a novel type of electronic devices. In contrast to conventional metals or semiconductors, this new class of materials exhibits peculiar transport properties at the sample surface, as conduction channels emerge at the topological boundaries of the system.
In specific materials with strong spin-orbit coupling, a particular form of a two-dimensional topological insulator, the quantum spin Hall state, can be observed.
Here, the respective one-dimensional edge channels are helical in nature, meaning that there is a locking of the spin orientation of an electron and its direction of motion.
Due to the symmetry of time-reversal, elastic backscattering off interspersed impurities is suppressed in such a helical system, and transport is approximately ballistic.
This allows in principle for the realization of novel energy-efficient devices, ``spintronic`` applications, or the formation of exotic bound states with non-Abelian statistics, which could be used for quantum computing.
The present work is concerned with the general transport properties of one-dimensional helical states. Beyond the topological protection mentioned above, inelastic backscattering can arise from various microscopic sources, of which the most prominent ones will be discussed in this Thesis. As it is characteristic for one-dimensional systems, the role of electron-electron interactions can be of major importance in this context.
First, we review well-established techniques of many-body physics in one dimension such as perturbative renormalization group analysis, (Abelian) bosonization, and Luttinger liquid theory. The latter allow us to treat electron interactions in an exact way.
Those methods then are employed to derive the corrections to the conductance in a helical transport channel, that arise from various types of perturbations.
Particularly, we focus on the interplay of Rashba spin-orbit coupling and electron interactions as a source of inelastic single-particle and two-particle backscattering. It is demonstrated, that microscopic details of the system, such as the existence of a momentum cutoff, that restricts the energy spectrum, or the presence of non-interacting leads attached to the system, can fundamentally alter the transport signature.
By comparison of the predicted corrections to the conductance to a transport experiment, one can gain insight about the microscopic processes and the structure of a quantum spin Hall sample.
Another important mechanism we analyze is backscattering induced by magnetic moments. Those findings provide an alternative interpretation of recent transport measurements in InAs/GaSb 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.
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.
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.