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Institute
Recently a new state of matter was discovered in which the bulk insulating state in a material is accompanied by conducting surface or edge states. This new state of matter can be distinguished from a conventional insulator phase by the topological properties of its band structure which led to the name "topological insulators". Experimentally, topological insulator states are mostly found in systems characterized by a band inversion compared to conventional systems. In most topological insulator systems, this is caused by a combination of energetically close bands and spin orbit coupling. Such properties are found in systems with heavy elements like Hg and Bi. And indeed, the first experimental discovery of a topological insulator succeeded in HgTe quantum wells and later also in BiSb bulk systems.
Topological insulators are of large interest due to their unique properties: In 2-dimensional topological insulators one dimensional edge states form without the need of an external magnetic field (in contrast to the quantum Hall effect). These edge states feature a linear band dispersion, a so called Dirac dispersion. The quantum spin Hall states are helical edge states, which means they consist of counterpropagating oppositely spin polarized edge channels. They are therefore of great potential for spintronic applications as well as building blocks for new more exotic states like Majorana Fermions. 3-dimensional topological insulators feature 2-dimensional surface states with only one Dirac band (also called Dirac cone) on each surface and an interesting spin texture where spin and momentum are locked perpendicular to each other in the surface plane. This unique surface band structure is predicted to be able to host several exotic states like e.g. Majorana Fermions (in combination with superconductors) and magnetic monopole like excitations.
This PhD thesis will summarize the discovery of topological insulators and highlights the developments on their experimental observations. The work focuses on HgTe which is up to now the only topological insulator material where the expected properties are unambiguously demonstrated in transport experiments. In HgTe, the topological insulator properties arise from the inversion of the Gamma_6 and Gamma_8 bands. The band inversion in HgTe is due to a combination of a high spin orbit splitting in Te and large energy corrections (due to the mass-velocity term) to the energy levels in Hg. Bulk HgTe, however, is a semimetal, which means for the conversion into a topological insulator a band gap has to be opened. In two dimensions (HgTe quantum well structures) this is achieved via quantum confinement, which opens a band gap between the quantum well subbands. In three dimensions, strain is used to lift the degeneracy of the semimetallic Gamma_8 bands opening up a band gap.
The thesis is structured as follows:
- The first chapter of this thesis will give a brief overview on discoveries in the field of topological insulators. It focuses on works relevant to experimental results presented in the following chapters. This includes a short outline of the early predictions and a summary of important results concerning 2-dimensional topological insulators while the final section discusses observations concerning 3-dimensional topological insulators.
- The discovery of the quantum spin Hall effect in HgTe marked the first experimental observation of a topological insulator. Chapter 2 will focus on HgTe quantum wells and the quantum spin Hall effect.
Above a critical thickness, HgTe quantum wells are predicted to host the quantum spin Hall state, the signature of a 2-dimensional topological insulator. HgTe quantum wells exhibiting low carrier concentrations and at the same time high carrier mobilities are required to be able to measure the quantum spin Hall effect. The growth of such high quality HgTe quantum wells was one of the major goals for this work. Continuous optimization of the substrate preparation and growth conditions resulted in controlled carrier densities down to a few 10^10 cm^-2. At the same time, carrier mobilities exceeding 1 x 10^6 cm^2/Vs have been achieved, which provides mean free paths of several micrometers in the material. Thus the first experimental evidence for the existence of the quantum spin Hall edge states succeeded in transport experiments on microstructures: When the Fermi energy was located in the bulk band gap a residual quantized resistance of 2e^2/h was found. Further experiments focused on investigating the nature of transport in this regime. By non-local measurements the edge state character could be established. The measured non-local resistances corresponded well with predictions from the Landauer-Büttiker theory applied to transport in helical edge channels.
In a final set of experiments the spin polarization of the edge channels was investigated. Here, we could make use of the advantage that HgTe quantum well structures exhibit a large Rashba spin orbit splitting. In systems with a large Rashba spin orbit splitting a spin accumulation is expected to occur at the edge of the sample perpendicular to a current flow. This so-called spin Hall effect was then used as a spin injector and detector. Using split gate devices it was possible to bring spin Hall and quantum spin Hall state into direct contact, which enabled an all electrical detection of the spin polarization of the quantum spin Hall edge channels.
- HgTe as a 3-dimensional topological insulator will be presented in chapter 3. Straining the HgTe layer enables the observation of topological insulator behavior. It was found that strain can be easily implemented during growth by using CdTe substrates. CdTe has a slightly larger lattice constant than HgTe and therefore leads to tensile strain in the HgTe layer as long as the growth is pseudomorphic. Magnetotransport studies showed the emergence of quantum Hall transport with characteristic signatures of a Dirac type bandstructure. Thus, this result marks the first observation of the quantum Hall effect in the surface states of a 3-dimensional topological insulator.
Transport experiments on samples fitted with a top gate enabled the identification of contributions from individual surfaces. Furthermore, the surface state quantum Hall effect was found to be surprisingly stable, perturbations due to additional bulk transport could not be found, even at high carrier densities of the system.
- Chapters 4 - 6 serve as in depth overviews of selected works: Chapter 4 presents a detailed overview on the all electrical detection of the spin Hall effect in HgTe quantum wells. The detection of the spin polarization of the quantum spin Hall effect is shown in chapter 5 and chapter 6 gives a detailed overview on the quantum Hall effect originating from the topological surface state in strained bulk HgTe.
The investigations discussed in this thesis pioneered the experimental work on the transport properties of topological insulator systems. The understanding of the fundamental properties of topological insulators enables new experiments in which e.g. the inclusion of magnetic dopants or the interplay between topological insulator and superconductors can be investigated in detail.
This thesis treats the thermopower and other thermal effects in single quantum dots (QD) and quantum dot systems. It contributes new experimental results to the broad and active field of research on thermoelectrics in low dimensional systems. The thermopower experiments discussed in this work focus on QDs which exhibit a net spin and on tunnel-coupled double QDs (DQD). Furthermore, experiments are presented which address the realization of a QD device which extracts thermal energy from a heat reservoir and converts it into a directed charge current in a novel way.
The samples used for these investigations have been fabricated from GaAs/AlGaAs heterostructures which contain a two dimensional electron gas. Using optical and electron beam lithography, the devices have been realized by means of the top-gate technology. All experiments have been performed at low temperature. In order to create a controllable temperature difference in the samples the current heating technique has been used. These experimental basics as well as fundamentals of electric and thermoelectric transport are introduced in Part I of this thesis.
The experiments on the thermopower of a single QD are described in Part II. Essentially, they deal with the problem of how a single spin situated on a QD influences the thermoelectric properties of the system. In this context, the Kondo-effect plays a crucial role. Generally, the Kondo effect is the result of a many-body state which arises from an antiferromagnetic coupling of a magnetic impurity with the surrounding conduction electrons. Here, the magnetic impurity is represented by a QD which is occupied with an odd number of electrons so that it exhibits a net spin. For the first time the thermopower of a Kondo-QD has been studied systematically as a function of two parameters, namely the QD coupling energy and the sample temperature. Both parameters are crucial quantities for Kondo-physics to be observed. Based on these data, it is shown that the thermopower line shape as a function of QD energy is mainly determined by two competing contributions: On the one hand by the enhanced density of states around the Fermi level due to Kondo-correlations and on the other hand by thermopower contributions from the Coulomb resonances. Furthermore, the experiments confirm theoretical predictions which claim that the spectral DOS arising from Kondo-correlations shifts away from the Fermi level for those QD level configurations which are not electron-hole symmetric. Comparison with model calculations by T. Costi and V. Zlatic [Phys. Rev. B 81, 235127 (2010)] shows qualitative and partly even quantitative agreement. A finite thermovoltage at the center of the Kondo-region, which occurred in previous investigations, is also observed in the experiments presented here. It is not covered by the current theory of the Kondo effect. The dependence of this signal on temperature, coupling energy and magnetic field, which differ from non-Kondo regions, is analyzed. In order to clarify the physics behind this phenomenon further studies are desirable.
Furthermore, it is shown by variation of the QD coupling energy over a wide range that Kondo-correlations can be detected in the thermopower even in the regime of very weak coupling. In contrast, no Kondo signatures are visible in the conductance in this energy range. It is found that in the limit of weak coupling the Kondo effect causes the thermopower to exhibit a diminished amplitude in close vicinity of a conductance resonance. Subsequent filling of spin-degenerate states then leads to a thermopower amplitude modulation (odd-even-effect). Although this effect had been observed in previous studies, no connection to Kondo physics had been established in order to explain the observations.
Hence, the experiments on a single QD presented in this thesis provide unique insight into the complex interplay of different transport mechanisms in a spin-correlated QD. Moreover, the results confirm the potential of thermopower measurements as a highly sensitive tool to probe Kondo-correlations.
In Part III thermal effects are investigated in systems which contain two coupled QDs.
Such QD-systems are particularly interesting with respect to thermoelectric applications: Many proposals utilize the extremely sharp energy filtering properties of such coupled QDs and also different kinds of inter dot coupling to construct novel and highly efficient thermoelectric devices. In the present work, thermopower characterizations are performed on a tunnel-coupled DQD for the first time. The key result of these investigations is the thermopower stability diagram. Here it is found, that in such a system maximal thermopower is generated in the vicinity of the so-called triple points (TP) at which three charge states of the DQD are degenerate. Along the axis of total energy, which connects two adjacent TP, a typical thermopower line shape is observed. It is explained and modeled within an intuitive picture that assumes two transport channels across the DQD, representing the TP. For those regions which are far away from the TP, the thermopower turns out to be very sensitive to the relative configuration of the QD energies. The conductance and thermopower data are well reproduced within a model that assumes transport via molecular states. Integration of both models into one then allows model calculations for a complete stability cell in conductance and thermopower to be done.
Furthermore, experiments on two capacitively coupled QDs are presented. In these studies the focus lies on testing the feasibility of such systems for the manipulation and generation of charge currents from thermal energy. In a series of experiments it is shown that such a system of QDs can be utilized to increase or decrease a current flowing between two electron reservoirs by varying the temperature in a third reservoir. This effect is based on the cross-correlation of occupation fluctuations of the individual QDs. These are positive for certain QD energy level configurations and negative for others, which increases or decreases the charge current in the experiments, respectively. In the stability diagram this is manifested in a characteristic clover leaf shaped structure of positive and negative current changes in vicinity of the TP. All main experimental results are reproduced qualitatively in simple model calculations. Due to the close analogy between electrical and thermal conductance of a QD, this effect of thermal switching can, in principle, also be used to built a thermal transistor.
Finally, it is shown that a system consisting of two Coulomb-coupled QDs, which couple a hot electron reservoir electrostatically to two cold electron reservoirs, can be utilized as a novel device which extracts heat from its environment and converts it into a directed charge current. The idea of this heat-to-current converter (HCC) was first proposed by R. Sánchez and M. Büttiker [Phys. Rev. B 83, 085428 (2011)]. It is not only characterized by the novelty of its working principle but also by the fact, that it decouples the directions of charge current and energy flow. In the experiments presented here, such HCC-currents are identified unambiguously: For certain QD-level configurations an electric current between the two cold reservoirs is observed if the temperature in the third reservoir is increased. The direction of this current is shown to be independent of an external voltage. In contrast, the direction of the current exhibits a characteristic dependence on the tunneling coefficients of the QDs, as predicted by theory: By adjusting the thickness and the shape of the respective tunnel junctions, a charge current can be generated between two cold reservoirs, and it can even be inverted. The experimental observations are quantitatively reproduced by model calculations by R. Sánchez and B. Sothmann. Thus, the results represent direct evidence for the existence of HCC-currents. Due to the novelty of the working principle of the HCC and its relevance from a fundamental scientific point of view, the results presented here are an important step towards energy harvesting devices at the nano scale.
Herstellung und Charakterisierung von Halbleiterbauelementen für die integrierte Quantenphotonik
(2014)
Der Schwerpunkt dieser Arbeit liegt auf der Entwicklung quantenphotonischer Komponenten, welche für eine monolithische Integration auf einem Halbleiter-Chip geeignet sind. Das GaAs-Materialsystem stellt für solch einen optischen Schaltkreis die ideale Plattform dar, weil es flexible Einzelphotonenquellen bereithält und mittels ausgereifter Technologien auf vielfältige Weise prozessiert werden kann.
Als Photonenemitter werden Quantenpunkte genutzt. Man kann sie mit komplexen Bauelementen kombinieren, um ihre optischen Eigenschaften weiter zu verbessern.
Im Rahmen dieser Arbeit konnte eine erhöhte Effizienz der Photonenemission beobachtet werden, wenn Quantenpunkte in Wellenleiter eingebaut werden, die durch photonische Kristalle gebildet werden. Die reduzierte Gruppengeschwindigkeit die diesem Effekt zugrunde liegt konnte anhand des Modenspektrums von kurzen Wellenleitern nachgewiesen werden. Durch zeitaufgelöste Messungen konnte ermittelt werden, dass die Zerfallszeit der spontanen Emission um einen Faktor von 1,7 erhöht wird, wenn die Emitter zur Mode spektrale Resonanz aufweisen. Damit verbunden ist eine sehr hohe Modeneinkopplungseffizienz von 80%.
Das Experiment wurde erweitert, indem die zuvor undotierte Membran des Wellenleiters durch eine Diodenstruktur ersetzt und elektrische Kontakte ergänzt wurden. Durch Anlegen von elektrischen Feldern konnte die Emissionsenergie der Quantenpunkte über einen weiten spektralen Bereich von etwa 7meV abgestimmt werden. Das Verfahren kann genutzt werden, um die exzitonischen Quantenpunktzustände in einen spektralen Bereich der Wellenleitermode mit besonders stark reduzierter Gruppengeschwindigkeit zu verschieben. Hierbei konnten für Purcell-Faktor und Kopplungseffizienz Bestwerte von 2,3 und 90% ermittelt werden. Mithilfe einer Autokorrelationsmessung wurde außerdem nachgewiesen, dass die Bauelemente als Emitter für einzelne Photonen geeignet sind.
Ein weiteres zentrales Thema dieser Arbeit war die Entwicklung spektraler Filterelemente. Aufgrund des selbstorganisierten Wachstums und der großen räumlichen Oberflächendichte von Quantenpunkten werden von typischen Anregungsmechanismen Photonen mit einer Vielzahl unterschiedlicher Energien erzeugt. Um die Emission eines einzelnen Quantenpunktes zu selektieren, muss der Transmissionsbereich des Filters kleiner sein als der Abstand zwischen benachbarten Spektrallinien. Ein Filter konnte durch die Variation des effektiven Brechungsindex entlang von indexgeführten Wellenleitern realisiert werden. Es wurde untersucht wie sich die optischen Eigenschaften durch strukturelle Anpassungen verbessern lassen. Ein weiterer Ansatz wurde mithilfe photonischer Kristalle umgesetzt. Es wurde gezeigt, dass der Filter hierbei eine hohe Güte von 1700 erreicht und gleichzeitig die Emission des Quantenpunkt-Ensembles abgetrennt werden kann. Die Bauelemente wurden so konzipiert, dass die im photonischen Kristall geführten Moden effizient in indexgeführte Stegwellenleiter einkoppeln können.
Ein Teil dieser Arbeit beschäftigte sich zudem mit den Auswirkungen von anisotropen Verspannungen auf die exzitonischen Zustände der Quantenpunkte. Besonders starke Verspannungsfelder konnten induziert werden, wenn der aktive Teil der Bauelemente vom Halbleitersubstrat abgetrennt wurde. Dies wurde durch ein neu entwickeltes Fabrikationsverfahren ermöglicht.
Infolgedessen konnten die Emissionsenergien reversibel um mehr als 5meV abgestimmt werden, ohne dass die optischen Eigenschaften signifikant beeinträchtigt wurden.
Die auf den aktiven Teil der Probe wirkende Verspannung wurde durch die Anwendung verschiedener Modelle abgeschätzt. Darüberhinaus wurde gezeigt, dass durch Verspannungen der spektrale Abstand zwischen den Emissionen von Exziton und Biexziton gezielt beeinflusst werden kann. Die Kontrolle dieser exzitonischen Bindungsenergie kann für die Erzeugung quantenmechanisch verschränkter Photonen genutzt werden. Dieses Ziel kann auch durch die Reduzierung der Feinstrukturaufspaltung des Exzitons erreicht werden. Die experimentell untersuchten Quantenpunkte weisen Feinstrukturaufspaltungen in der Größenordnung von 100meV auf. Durch genau angepasste Verspannungsfelder konnte der Wert erheblich auf 5,1meV verringert werden. Beim Durchfahren des Energieminimums der Feinstrukturaufspaltung wurde eine Drehung der Polarisationsrichtung um nahezu 90° beobachtet. Desweiteren wurde ein Zusammenhang des Polarisationsgrades mit der Feinstrukturaufspaltung nachgewiesen.
Es wurde ein weiterer Prozessablauf entworfen, um komplexe Halbleiterstrukturen auf piezoelektrische Elemente übertragen zu können. Damit war es möglich den Einfluss der Verspannungsfelder auf Systeme aus Quantenpunkten und Mikroresonatoren zu untersuchen. Zunächst wurde demonstriert, dass die Modenaufspaltung von Mikrosäulenresonatoren reversibel angepasst werden kann. Dies ist ebenfalls von Interesse für die Erzeugung polarisationsverschränkter Photonen. An Resonatoren aus photonischen Kristallen konnte schließlich gezeigt werden, dass das Verhältnis der spektralen Abstimmbarkeiten von exzitonischen Emissionslinien und Resonatormode etwa fünf beträgt, sodass beide Linien in Resonanz gebracht werden können. Dieses Verhalten konnte zur Beeinflussung der Licht-Materie-Wechselwirkung genutzt werden.