Transport Spectroscopy of Confined Fractional Quantum Hall Systems (eBook)

Stephan Baer, Klaus Ensslin (Autoren)

eBook Download: PDF

2015 | 1st ed. 2015
XIV, 308 Seiten
Springer International Publishing (Verlag)
978-3-319-21051-3 (ISBN)

Infos

This book provides an overview of recent developments in experiments probing the fractional quantum Hall (FQH) states of the second Landau level, especially the nu=5/2 state. It summarizes the state-of-the-art understanding of these FQH states. It furthermore describes how the properties of the FQH states can be probed experimentally, by investigating tunneling and confinement properties. The progress towards the realization of an experiment, allowing to probe the potentially non-Abelian statistics of the quasiparticle excitations at nu=5/2 is discussed. The book is intended as a reference for graduate students, PostDocs and researchers starting in the field. The experimental part of this book gives practical advice for solving the experimental challenges which researchers studying highly fragile FQH states are faced with.

Stephan Baer studied physics at ETH Zürich and at the ENS Paris. He was awarded an ETH medal for his MSc work on electron-phonon interaction in graphene nanostructures. During his PhD, he investigated the properties of fractional quantum Hall states in confined geometries, such as quantum point contacts, quantum dots and interferometers. The emphasis of this work lies on exploring the properties of exotic fractional quantum Hall states, like the nu = 5/2 state. Since 2014, he continues his research at ETH Zürich as a PostDoc.

Klaus Ensslin received his bachelor's degree from the University of Munich in 1983 and bis master's degree from ETH Zurich in 1986. He did his PhD at the Max-Planck Institute for Solid State Research in Stuttgart followed by a postdoc at the University of California in Santa Barbara 1989-91. After several years as a university assistant at the University of Munich he became professor at ETH Zurich in 1995 and has stayed there every since. In 2011 Klaus Ensslin became director of the National Center of Competence in Research on 'Quantum Science and Technology'.

Inhalt

Preface 6
Contents 8
Symbols and Abbreviations 14
1 Introduction 16
References 20
Part IFundamentals of Quantum Hall Physicsand Relevant Experiments 21
2 Two-Dimensional Electron Gases 22
2.1 Introduction 22
2.2 Basic Properties of Two-Dimensional Electron Gases 23
2.3 Low Field Magnetoresistance of Two-Dimensional Electron Gases 27
2.4 Growth Schemes for High Electron Mobilities 29
2.5 Impact of Disorder on the Gap of the ?=5/2 State 31
References 33
3 The Quantum Hall Effect 34
3.1 Introduction 34
3.2 Energy Spectrum in a Magnetic Field 34
3.3 Shubnikov-De Haas Effect 37
3.4 Integer Quantum Hall Effect 38
3.4.1 Landauer-Büttiker Formalism 39
3.4.2 Many-Body Wavefunction of the Lowest Landau Level 42
3.5 Fractional Quantum Hall Effect 42
3.5.1 Laughlin's Wavefunction 43
3.5.2 Composite Fermion Theory 44
3.6 Fractional Quantum Hall Effect in the Second Landau Level 47
3.6.1 Candidate States for /nu = 5/2 48
3.6.2 Candidate States for /nu = 7/3 and /nu = 8/3 52
3.6.3 Candidate States for /nu = 12/5 54
3.7 Conclusion 56
References 56
4 Physics at the Edge 59
4.1 Introduction 59
4.2 Spatial Edge State Picture 59
4.2.1 Self-consistency at the Edge 60
4.2.2 FQH Edge States 62
4.3 Energetic Edge State Picture 67
4.3.1 Hydrodynamic Theory 67
4.3.2 Hierarchical States and Bulk-Edge Correspondence 70
4.3.3 Tunneling in a QPC 70
References 73
5 Non-Abelian Statistics and Its Signatures in Interference Experiments 74
5.1 From Fermions to Anyons 74
5.2 Non-Abelian Anyons in the Moore-Read Pfaffian State 75
5.3 Interferometry with Non-Abelian Anyons 77
5.4 Aharonov-Bohm Versus Coulomb-Dominated Physics 78
References 81
6 Overview of Experiments Probing the Properties of the ? = 5/2 State 83
6.1 Introduction 83
6.2 Numerical Studies 84
6.3 Detecting the Quasiparticle Charge 85
6.3.1 Shot Noise Measurements 85
6.3.2 Local Compressibility Measurements 86
6.4 Bulk Experiments: Probing the Spin Polarization 86
6.4.1 Transport: Density Dependence of the Gap 87
6.4.2 Transport: In-Plane Magnetic Fields 89
6.4.3 Optics 90
6.4.4 Nuclear Magnetic Resonance Techniques 91
6.4.5 Conclusion 92
6.5 Probing the Edge Properties 92
6.5.1 Quasiparticle Tunneling 92
6.5.2 Neutral Mode Experiments 94
6.6 Interference Experiments at ? = 5/2 96
6.7 Summary 100
References 101
Part IISetup and Sample Optimization 104
7 Measurement Setup Optimization for Low Electron Temperatures 105
7.1 Introduction 105
7.2 Dilution Refrigerator Setup 106
7.2.1 Vibration Minimization and Insulation 109
7.2.2 Electronic Noise 114
7.3 Cryostat Cabling and Cold Filtering 116
7.3.1 General Remarks 116
7.3.2 Thermocoax Cables 119
7.3.3 ?-Filters 119
7.3.4 Quartz Heat Sinks 120
7.3.5 RC Low-Pass Filters 121
7.3.6 Silver Cold-Finger 121
7.3.7 Filter Attenuation 123
7.4 Estimation of the Electronic Temperature 125
7.5 Outlook 128
7.6 Conclusion 129
References 129
8 Optimization of Samples and Sample Fabrication 131
8.1 Introduction 131
8.2 Non-invasive Processing 131
8.3 Mesa and Contact Geometry 133
8.4 Ohmic Contacts and Contact Resistance 135
8.5 Conclusion 137
References 137
Part IIIQuantum Point Contact Experiments 138
9 Quantum Point Contacts 139
9.1 Introduction 139
9.2 Conductance of Ideal and Non-ideal QPCs 141
9.2.1 Transmission of an Ideal Quantum Wire 141
9.2.2 Non-ideal QPC 143
9.2.3 Saddle-Point Potential 144
9.2.4 Magneto-Electric Depopulation 145
9.3 QPC Simulations 145
9.4 Transport Properties of Clean QPCs 148
9.4.1 Lateral Shifting of the QPC Channel 148
9.4.2 Finite Bias Transmission 149
9.4.3 Tuning the QPC Confinement Potential 153
9.4.4 Spin-Resolved Transport 157
9.4.5 Bias Dependence in the Quantum Hall Regime 159
9.5 Conclusion 161
References 162
10 Integer and Fractional Quantum Hall States in QPCs 164
10.1 Introduction 164
10.2 Experimental Details 166
10.3 Results and Discussion 167
10.3.1 Quantum Hall Phase Diagram of a QPC 167
10.3.2 Influence of QPC Geometry on Incompressible Separating Region and Density Distribution 170
10.3.3 Characterization of QPC Resonances and Microscopic Model 172
10.3.4 Spatial Dependence of QPC Resonances 179
10.3.5 Fragile Fractional Quantum Hall States in QPCs 182
10.3.6 Energy Gap of the ?QPC = 1/3 State 185
10.4 Conclusion 188
References 189
11 Quasiparticle Tunneling in the Second Landau Level 192
11.1 Introduction 192
11.2 Experimental Details 194
11.3 Measurement Results 194
11.3.1 Tunneling Conductance at /nu = 5/2 196
11.3.2 Tunneling Conductance at /nu = 8/3 200
11.3.3 Effect of Varying the Coupling via the Magnetic Field 202
11.3.4 Effect of Varying the Coupling via the QPC Transmission 205
11.3.5 Breakdown of the Weak Tunneling Regime 206
11.4 Interpretation and Discussion 207
11.4.1 /nu = 8/3 207
11.4.2 /nu = 5/2 208
11.4.3 /nu = 7/3 209
11.4.4 Experimental Limitations and Origin of Systematic Errors 210
11.5 Conclusion 211
References 220
Part IVQuantum Dot and InterferometerExperiments 224
12 Quantum Dots and Charge Detection Techniques 225
12.1 Introduction 225
12.2 Basics of Quantum Dots 226
12.2.1 Energy Scales 226
12.2.2 Coulomb Blockade 227
12.2.3 Principle of Charge Detection 229
12.3 Improving the Charge Detection Sensitivity 230
12.4 Conclusion 234
References 235
13 Quantum Dots in the Quantum Hall Regime 237
13.1 Introduction 237
13.2 Experimental Details 238
13.3 Results and Discussion 239
13.3.1 Zero Magnetic Field Transport 239
13.3.2 Non-cyclic Depopulation of Edge Channels 239
13.3.3 Transport in the Fabry-Pérot Regime 247
13.4 Conclusion 249
References 249
14 Preliminary Results of Interference Experiments in the Second Landau Level 251
14.1 Introduction 251
14.2 Design Considerations 252
14.3 Transport Measurements 254
14.3.1 Sample Stability Issues 255
14.3.2 Optimizing the Transmission by Sample Illumination 257
14.4 Conclusion and Outlook 265
References 265
Part VBulk Transport Experiments 267
15 Non-equilibrium Transport in Density Modulated Phases of the Second Landau Level 268
15.1 Introduction 268
15.2 Experimental Details 269
15.3 Results and Discussion 270
15.3.1 Phase Diagram of Reentrant Integer Quantum Hall Phases 272
15.3.2 Transition from RIQH Phase to Isotropic Compressible Phase 274
15.3.3 Discussion of the Bias Dependence 277
15.3.4 Reentrant Integer Quantum Hall Phases in a QPC 279
15.3.5 Orientation Dependence 281
15.4 Conclusion 282
References 286
Part VIConclusion 289
16 Conclusion 290
Appendices 293
Index 305

Produkt-Details

• Erscheint lt. Verlag: 18.8.2015
• Reihe/Serie: Springer Series in Solid-State Sciences
• Reihe/Serie: Springer Series in Solid-State Sciences
• Zusatzinfo: XIV, 308 p. 153 illus., 116 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Exotic fractional quantum Hall states • Interferometer experiments • Non-abelian statistics • Non-equilibrium transport • /nu = 5/2 state • Quantum dot and interferometer • Quantum dot experiments • Quantum Hall Effect • Quantum point contact experiments • Quantum Point Contacts • Two-dimensional electron gases
• ISBN-10: 3-319-21051-3 / 3319210513
• ISBN-13: 978-3-319-21051-3 / 9783319210513