Quanten-Hall-Systeme in hohen Landau-Niveaus

Title Page and Front Matter Table of Contents i 1\. Introduction 1 1.1 The Integer Quantum Hall Effect 1 1.2 The Fractional Quantum Hall Effect 2 1.3 High Landau Levels 9 1.4 This Thesis 11 2\. Microwave-Induced Zero Resistance States 15 2.1 Zero Resistance States and Microwave-Induced Resistance Oscillations 15 2.2 Theoretical Explanation of ZRS 17 3\. Classical Model for a Microwave-Irradiated 2DEG in the Presence of Bichromatic Irradiation 27 3.1 Monochromatic Irradiation 28 3.2 Bichromatic Irradiation 31 3.3 Bichromatic Irradiation and Absolute Negative Conductivity 45 3.4 Discussion 46 4\. Microwave Photoconductivity due to Intra-Landau-Level Transitions 49 4.1 Experiment 50 4.2 Model 51 4.3 Mechanisms 60 4.4 Dark Current 66 4.5 Photocurrent 68 4.6 Comparison with Experiment 77 4.7 Polarization Dependence 79 4.8 Discussion 80 5\. In-Plane Magnetic Field 83 5.1 Theory 84 5.2 Results 92 5.3 Discussion 94 6\. Drag in Double-Layer Systems 97 6.1 Conventions 98 6.2 Coulomb Drag 100 6.3 Phonon Drag 102 6.4 Linear Response Theory of Drag 104 7\. Phonon Drag in High Landau Levels 109 7.1 Linear Response Theory of Phonon Drag: Triangle Vertex and Polarization Function 109 7.2 Interaction of 2D Electrons with Bulk Phonons in the Bilayer System 117 7.3 Analytical Results 124 7.4 Numerical Results 131 7.5 Discussion 139 8\. Conclusions 141 Appendix 145 Acknowledgments 175 Bibliography 179 Abstract Citations of previously published workIn recent years, the experimental study of quantum Hall systems in weak magnetic fields has yielded unexpected and interesting discoveries. In this thesis, we focus on the two most interesting phenomena observed in magnetotransport experiments on such systems: (i) zero resistance states in microwave-irradiated high mobility samples and (ii) drag between parallel two- dimensional electron gases (2DEG) in double-layer samples. The diagonal resistivity of a 2DEG in an ultraclean GaAs/AlGaAs heterostructure subjected to microwave radiation exhibits magnetooscillations whose minima, for sufficiently high microwave power, can evolve into zero resistance states (ZRS) within specific ranges of magnetic field. Intriguingly, the zeros in the diagonal resistivity are not accompanied by plateaus in the Hall resistivity, which would be characteristic of a quantum Hall state. The first part of this thesis is devoted to the physics of these ZRS. We first examine the special case of bichromatic irradiation and show that the emergence of ZRS can be explained within a classical model. In addition, we predict interesting novel effects under bichromatic irradiation and present a way to parametrically excite the cyclotron mode by bichromatic irradiation. We argue that bichromatic irradiation can be used as a tool to verify absolute negative local conductivity, which lies at the center of the theoretical explanation of ZRS within a microscopic quantum mechanical model. We then present a microscopic theory for the recently discovered magnetooscillations for microwave frequencies smaller than the cyclotron frequency. We formulate a microscopic model which mimics the effect of a smooth random disorder potential by the introduction of a periodic modulation and calculate the conductivity under microwave irradiation. We are able to explain why no ZRS are observed in this intra-Landau-level regime and explain the experimentally observed suppression of Shubnikov-deHaas oscillations. We reproduce the sign of the photoconductvity, its magnetic field and frequency dependence as well as its filling factor dependence in excellent qualitative agreement with experiment. We also discuss the application of an in-plane magnetic field to a highmobility 2DEG under microwave irradiation, which has been demonstrated experimentally to induce a pronounced suppression or even destruction of the ZRS. We calculate the effect of a tilted magnetic field within a kinetic approach for spin-split Landau bands and estimate the relevance of Zeeman splitting for the suppression of the ZRS. The second part of this work is devoted to the physics of drag phenomena in bilayer quantum Hall systems at weak magnetic fields, more specifically to phonon drag, which, in contrast to the well-studied Coulomb drag, had not been understood within a microscopical theory. We develop the linear response theory for the phonon drag conductivity by extending an established approach for Coulomb drag. The main difference between Coulomb and phonon drag is due to the specific form of the phonon- mediated interlayer interaction, which, in contrast to the Coulomb interlayer interaction, allows for a larger range of momentum transfers between the layers of the bilayer system. We derive the phonon-mediated interlayer interaction in polar semiconductors such as GaAs and calculate the phonon contribution to the drag conductivity in the experimentally relevant regime. We finally present numerical results for the drag resistivity within a variety of parameter ranges.In den letzten Jahren hat die experimentelle Untersuchung von Quanten-Hall- Systemen in schwachen Magnetfeldern unerwartete und interessante Entdeckungen hervorgebracht. In dieser Doktorarbeit wenden wir uns den zwei interessantesten Phänomenen zu, die in Magnetotransportmessungen an solchen Systemen beobachtet werden: (i) den widerstandslosen Zuständen in mikrowellenbestrahlten, hochreinen Systemen und (ii) dem sog. "Drag"-Effekt (Zugeffekt) zwischen zueinander parallelen zweidimensionalen Elektronengasen (2DEG) in Doppelschichtsystemen. Der diagonale relative Widerstand eines 2DEG in einer hochreinen GaAs/ AlGaAs-Heterostruktur zeigt unter Bestrahlung mit Mikrowellen Magnetooszillationen, deren Minima für genügend große Mikrowellenleistung innerhalb bestimmter Magnetfeldbereiche in widerstandslose Zustände, sog. zero resistance states (ZRS), übergehen können. Faszinierenderweise werden diese Nullstellen im diagonalen relativen Widerstand nicht von Plateaus im Hall-Widerstand begleitet, wie es für Quanten-Hall-Zustände charakteristisch wäre. Der erste Teil dieser Arbeit widmet sich der Physik dieser ZRS. Zunächst untersuchen wir den Spezialfall bichromatischer Bestrahlung und zeigen, daß das Auftreten von ZRS im Rahmen eines klassischen Modells erklärt werden kann. Außerdem sagen wir interessante neuartige Effekte voraus, die bei bichromatischer Bestrahlung auftreten und stellen eine Methode vor, mit der die Zyklotronmode mittels bichromatischer Bestrahlung parametrisch angeregt werden kann. Wir zeigen, wie bichromatische Bestrahlung dazu benutzt werden kann, absolut negative Leitfähigkeit nachzuweisen. Diese nimmt in der theoretischen Beschreibung der ZRS im Rahmen eines mikroskopischen quantenmechanischen Modells eine zentrale Rolle ein. Sodann entwickeln wir eine mikroskopische Theorie für das kürzlich unter Bestrahlung mit Mikrowellenfrequenzen unterhalb der Zyklotronfrequenz entdeckte Auftreten von Magnetooszillationen. Wir formulieren ein mikroskopisches Modell, das den Effekt eines glatten Zufalls- Unordnungspotentials mittels einer periodischen Modulation nachahmt und berechnen den Leitwert unter Mikrowellenbestrahlung. Dies ermöglicht uns zu erklären, warum für dieses Intra- Landauniveau-Regime keine ZRS beobachtet werden und wie die experimentell beobachtete Unterdrückung der Shubnikov- deHaas-Oszillationen entsteht. Wir sind in der Lage, das Vorzeichen des Leitwerts, seine Magnetfeld- und Frequenzabhängigkeit sowie den Zusammenhang mit dem Füllfaktor in hervorragender qualitativer Übereinstimmung mit dem Experiment zu bestimmen. Zudem diskutieren wir den Einfluß eines zur Ebene des 2DEG parallelen Magnetfelds auf ein hochreines, mit Mikrowellen bestrahltes 2DEG. Experimentell beobachtet man in diesem Fall eine Unterdrückung oder gar Zerstörung der ZRS. Wir berechnen die Auswirkungen eines gekippten Magnetfeldes im Rahmen einer kinetischen Theorie spinaufgespaltener Landau- Bänder und schätzen die Rolle der Zeeman-Aufspaltung für die Unterdrückung der ZRS ab. Der zweite Teil dieser Arbeit befasst sich mit der Physik von Drag- Phänomenen in Doppelschicht-Quanten-Hall-Systemen bei schwachen Magnetfeldern. Genauer beschäftigen wir uns mit phononenvermitteltem Drag, der bislang im Gegensatz zum weitgehend verstandenen, durch Coulomb-Wechselwirkung vermittelten Drag noch nicht durch eine mikroskopische Theorie beschrieben werden konnte. Wir entwickeln die lineare Antworttheorie für den Phonon- Drag- Leitwert, indem wir eine für Coulomb-Drag bewährte Herangehensweise erweitern. Der Hauptunterschied zwischen Coulomb-Drag und Phonon-Drag liegt in der spezifischen Form der phononenvermittelten Wechselwirkung zwischen den beiden Schichten. Im Gegensatz zur Coulomb-Wechselwirkung gestattet die phonenvermittelte Wechselwirkung einen größeren Bereich von Impulsüberträgen zwischen den Schichten des Doppelschicht-Systems. Wir leiten die phononenvermittelte Wechselwirkung in polaren Halbleitern wie z.B. GaAs her und berechnen den phononenvermittelten Beitrag zum Drag-Leitwert im experimentell relevanten Parameterbereich. Abschließend stellen wir numerische Resultate für den spezifischen Drag-Widerstand in einer Vielzahl weiterer Parameterbereiche vor

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