Schreiber Ground States of the Two-Dimensional Electron System at Half-Filling under Hydrostatic Pressure

1. Auflage 2019
ISBN: 978-3-030-26322-5
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 112 Seiten

Reihe: Springer Theses

This thesis presents the discovery of a surprising phase transition between a topological and a broken symmetry phase. Phase transitions between broken symmetry phases involve a change in symmetry and those between topological phases require a change in topological order; in rare cases, however, transitions may occur between these two broad classes of phases in which the vanishing of the topological order is accompanied by the emergence of a broken symmetry. This thesis describes observations of such a special phase transition in the two-dimensional electron gas confined in the GaAs/AlGaAs structures. When tuned by hydrostatic pressure, the ? = 5/2 and ? = 7/2 fractional quantum Hall states, believed to be prototypical non-Abelian topological phases of the Pfaffian universality class, give way to an electronic nematic phase. Remarkably, the fractional quantum Hall states involved are due to pairing of emergent particles called composite fermions. The findings reported here, therefore, provide an interesting example of competition of pairing and nematicity. This thesis provides an introduction to quantum Hall physics of the two-dimensional electron gas, contains details of the high pressure experiments, and offers a discussion of the ramifications and of the origins of the newly reported phase transition.

Katherine Schreiber is a postdoctoral researcher at the National High Magnetic Field Laboratory at Los Alamos National Laboratory. She received her PhD from Purdue University in 2018.

Autoren/Hrsg.

Schreiber, Katherine A.

Inhaltsverzeichnis

1;Supervisor's Foreword;6
2;Acknowledgments;8
3;Contents;10
4;Parts of this thesis have been published in the following journal articles;13
5;1 The Quantum Hall Effect;14
5.1;1.1 Two-Dimensional Electron Systems;14
5.2;1.2 Classical Hall Effect;17
5.3;1.3 Two-Dimensional Electron Systems in a Magnetic Field;19
5.4;1.4 Integer Quantum Hall Effect;21
5.5;1.5 Fractional Quantum Hall Effect;24
5.5.1;1.5.1 Quasiparticles in the Fractional Quantum Hall Effect: Fractional Charge and Fractional Statistics;27
5.5.2;1.5.2 The Composite Fermi Sea at ?= 1/2, 3/2;28
5.5.3;1.5.3 The Quantum Hall Effect and Topological Order;28
5.6;1.6 ?= 5/2 Fractional Quantum Hall State;29
5.6.1;1.6.1 Current Experimental Status of the ?= 5/2 Fractional Quantum Hall State;31
5.6.1.1;Gap of the ?=5/2 Fractional Quantum Hall State;31
5.6.1.2;Spin Polarization Studies;31
5.6.1.3;Shot Noise and the Quasiparticle Charge;32
5.6.1.4;Tunneling Conductance Through a Quantum Point Contact;33
5.6.1.5;Quantum Hall Interferometry;34
5.6.2;1.6.2 ?= 7/2 Fractional Quantum Hall State;34
5.7;1.7 Conclusion;35
5.8;References;35
6;2 The Quantum Hall Nematic Phase;38
6.1;2.1 Nematicity in Condensed Matter Systems;38
6.2;2.2 Prediction and Theory of the Nematic State in the Two-Dimensional Electron System;40
6.3;2.3 Experimental Observation of the Nematic Phase: ?= 9/2, 11/2, 13/2...;40
6.4;2.4 The Effect of In-Plane Magnetic Field on the Nematic at ?= 9/2, 11/2, 13/2...;41
6.5;2.5 The Effect of In-Plane Magnetic Field on the Second Landau Level Fractional Quantum Hall States;42
6.5.1;2.5.1 Nematic Fractional Quantum Hall States: ?=7/3 and ?= 5/2;43
6.6;2.6 Recent Studies of the Nematic Phase;44
6.7;2.7 Other Anisotropic Signatures in Even Denominator States;45
6.8;2.8 Electron Solids: Wigner Crystal and Bubble Phases;45
6.9;2.9 Summary of States at Half-Filling;46
6.10;2.10 Conclusion;47
6.11;References;48
7;3 Low Temperature Measurement Techniques;50
7.1;3.1 Dilution Refrigeration;50
7.2;3.2 Low Noise Electronics;54
7.3;3.3 Conclusion;55
7.4;References;55
8;4 The Quantum Hall Effect and Hydrostatic Pressure;56
8.1;4.1 Gallium Arsenide Under Pressure;56
8.2;4.2 Previous Experiments of the Fractional Quantum Hall Effect Under Pressure;59
8.3;4.3 Pressure Clamp Cell;60
8.3.1;4.3.1 Diamond Anvil Cells;62
8.4;4.4 Preparing for Pressurization and Cooldown;63
8.4.1;4.4.1 Mounting the Sample to Pressure Cell Feedthrough;63
8.5;4.5 Monitoring the Effect of Pressure;66
8.5.1;4.5.1 Room Temperature Pressure Monitoring;66
8.5.2;4.5.2 Low Temperature Pressure Monitoring;68
8.6;4.6 Conclusion;71
8.7;References;71
9;5 The Fractional Quantum Hall State-to-Nematic Phase Transition Under Hydrostatic Pressure;73
9.1;5.1 Observation of the Fractional Quantum Hall State-to-Nematic Transition at ?= 5/2;74
9.2;5.2 Spontaneous Rotational Symmetry Breaking;77
9.3;5.3 Topology, Pairing, and the Nematic Phase;79
9.4;5.4 Finite Temperature Studies at ?= 5/2;80
9.5;5.5 Quantum Phase Transition from Nematic Phase to Fermi Fluid-Like Phase;85
9.6;5.6 Conclusion;86
9.7;References;87
10;6 Universality of the Fractional Quantum Hall State-to-Nematic Phase Transition at Half-Filling in the Second Landau Level;89
10.1;6.1 Observation of the FQHS-to-Nematic Phase Transitionat ?= 7/2;89
10.2;6.2 Finite Temperature Studies at ?= 5/2 and ?= 7/2;94
10.3;6.3 Conclusion;100
10.4;References;100
11;7 Origin of the Fractional Quantum Hall State-to-Nematic Phase Transition in the Second Landau Level;102
11.1;7.1 Tuning the Electron–Electron Interactions with Landau Level Mixing;102
11.2;7.2 Tuning the Electron–Electron Interactions Through Quantum Well Width;103
11.3;7.3 The Role of Electron–Electron Interactions in the Fractional Quantum Hall State-to-Nematic Phase Transition;104
11.4;7.4 Observation of the Nematic Phase at ?= 7/2 at AmbientPressure;107
11.5;7.5 Recent Theory of the Transitions to the Nematic Phase;109
11.6;7.6 Importance of the Second Landau Level for the FQHS-to-Nematic Phase Transition;109
11.7;7.7 Conclusion;111
11.8;References;111