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

:	Katherine A. Schreiber
:	Ground States of the Two-Dimensional Electron System at Half-Filling under Hydrostatic Pressure
:	Springer-Verlag
:	9783030263225
:	1
:	CHF 85.60
:

:	Atomphysik, Kernphysik
:	English

:	112
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

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.

	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