Ground States of the Two-Dimensional Electron System at Half-Filling under Hydrostatic Pressure (eBook)

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