Emergent Superconductivity in Low Dimensions (eBook)

Dr. Diane Ansermet completed her Bachelor’s and Master’s degrees at EPFL in Switzerland, where she studied Materials Sciences and Engineering. The equal contributions of physics, chemistry, and engineering were a great foundation for this young woman with an unquenchable thirst for learning. Her passion for physics started with the discovery of quantum mechanics, where invisible phenomena govern modern technologies. This new passion was coupled with her love for travelling and an increasing interest in Asian cultures and geography, and she moved to Nanyang Technological University in Singapore to complete her Master’s thesis in the field of semiconductor nanowires. It was here that she was introduced to the wonderful world of low-dimensional superconductivity, and her journey became filled with novel discoveries and great collaborations.

Supervisor’s Foreword 7
Abstract 8
Parts of this thesis have been published in the following journal articles: 9
Declaration of Authorship 10
Acknowledgements 11
Contents 13
Abbreviations 17
Symbols 19
List of Figures 21
List of Tables 33
Physical ConstantsBohr magneton /mu_{B} = e/hbar /2m_{e} c /approx 9.274 /times 10^{ - 24} J/TBoltzmann constant k_{B} /approx 1.381 /times 10^{ - 23} J/KElectron charge e /approx 1.602 /times 10^{ - 19} CElectron mass m_{e} /approx 9.109 /times 10^{ - 31} kgMagnetic flux quantum /Phi_{0} /equiv /frac{h}{2e} /approx 2.067 /times 10^{ - 15} WbPlanck’s constant h /approx 6.626 /times 10^{ - 34} Js /hbar = h/2/pi /approx 1.054 /times 10^{ - 34} JsSpeed of light c /approx 2.997 /times 10^{8} m/sVacuum permeability /mu_{0} = 4/pi /times 10^{ - 7} N/A2 34
1 Superconductivity: History and Motivations 35
1.1 History 35
1.2 Motivations: A Fresh Look Towards Functional Superconductors 36
References 37
2 Introduction and Theory 39
2.1 Superconductivity 39
2.1.1 Experimental Signatures of Superconductivity 39
2.1.2 A Macroscopic Quantum Phenomenon 39
2.1.3 Bardeen–Cooper–Schrieffer Theory 41
2.1.4 Ginzburg–Landau Theory: the Complex Order Parameter 44
2.2 Superconductivity in Low Dimensions 46
2.2.1 One-Dimensional Phase Fluctuations 47
2.2.2 Quasi-One-Dimensional Superconductors 51
2.2.3 Superconducting Transition in a Quasi-One-Dimensional System 54
2.3 Josephson Coupling 56
2.3.1 The Josephson Junction and Critical Current 56
2.3.2 The Josephson Energy 57
2.3.3 Internal Josephson Junctions in Low-Dimensional Superconductors 58
2.4 Disorder and Superconductivity 58
2.4.1 Electron Localization in Three Dimensions 59
2.4.2 Anderson Theorem 61
2.4.3 Metal-Insulator Transition in Two Dimensions 61
2.4.4 New Approaches and Theories 63
References 64
3 Experimental Methods 67
3.1 The Dilution Refrigerator 67
3.1.1 Mixture Circulation and Condensation 69
3.1.2 Thermal Isolation and Radiation Shielding 72
3.1.3 Mixture Cleaning 75
3.1.4 Mixture Circulation Control and Monitoring 75
3.1.5 Electrical Connections 76
3.1.6 Measurement Probes 78
3.2 The Variable Temperature Insert 80
3.2.1 Helium Condensation and Circulation 80
3.2.2 Thermal Isolation and Radiation Shielding 81
3.2.3 Helium Gas Cleaning 83
3.2.4 Electrical Connections 83
3.2.5 Measurement Probe 85
3.3 Superconducting Magnets 85
3.3.1 Superconducting Magnet Materials 86
3.3.2 Stored Energy and Forces in a Magnet 86
3.3.3 Magnet Specifications 87
3.3.4 Operating Modes 90
3.3.5 Electrical Connections 90
3.4 Helium Recovery and Re-Liquefying Systems 90
3.5 Electronics 92
3.5.1 Electronics Description 93
3.5.2 Electrical Noise Filtering 95
3.6 Automated Measurement Systems 96
3.6.1 The Physical Property Measurement System 96
3.6.2 The Magnetic Property Measurement System 98
3.7 Sample and Contacts Preparation 99
3.7.1 Sample Growth 99
3.7.2 Electrical Contact Preparation 101
3.7.3 Transport Measurement Details 104
References 104
4 The Quasi-One-Dimensional Na2-?Mo6Se6 106
4.1 Introduction 106
4.2 The M2-?Mo6Se6 Family 107
4.2.1 The Insulating Compounds 108
4.2.2 The Superconducting Compounds 109
4.2.3 The Intermediate Compound Na2-?Mo6Se6 110
4.3 Structural Properties 111
4.3.1 Crystal Structure 111
4.3.2 Intrinsic Disorder from Na Vacancies 112
4.4 Electronic Properties 113
4.4.1 Band Structure 113
4.4.2 Anisotropic Evolution in the M2-?Mo6Se6 Family 117
4.4.3 Anisotropic Random Resistor Network 118
References 120
5 The Electronic Normal State in Na2-?Mo6Se6 123
5.1 Introduction 123
5.2 General Observations 123
5.2.1 Intrinsic Disorder in Na2-?Mo6Se6 126
5.3 Luttinger Liquid in the High Temperature Regime 126
5.3.1 Theory of the Luttinger Liquid 127
5.3.2 Fits to the Luttinger Liquid Model 127
5.3.3 Renormalized Energy Scales in a Disordered System 128
5.4 Metal-Insulator Transition in the Intermediate Temperature Regime 131
5.4.1 Mechanisms for the Metal-Insulator Transition 131
5.4.2 Fits to the Variable Range Hopping Model 132
5.4.3 Signatures of Anderson Localization 135
5.4.4 Emergence of a Mobility Edge 139
5.5 Concluding Remarks 141
References 141
6 Superconducting Transition and Pairing Enhancement by Disorder 144
6.1 Introduction 144
6.2 Identifying Superconductivity in Na2-?Mo6Se6 145
6.3 The Superconducting Transition 147
6.3.1 Emergence of 1D Phase-Fluctuating Superconductivity 147
6.3.2 Establishment of a Coherent Superconducting State 149
6.4 Pairing Enhancement 153
6.4.1 Possible Mechanism for the Enhancement of Superconductivity 158
6.5 Concluding Remarks 161
References 162
7 Reentrant Phase Coherence by Josephson Coupling 165
7.1 Introduction 165
7.2 Reentrant Superconductivity: A Short Overview 166
7.2.1 Reentrant Superconductivity by Josephson Coupling 166
7.2.2 Reentrant Superconductivity by Other Mechanisms 168
7.3 Experimental Study of the Superconducting State 170
7.3.1 Further Investigation of the 1D Superconducting Transition 170
7.3.2 Observations of Reentrant Phase Coherence 171
7.4 Analysis 175
7.4.1 Determination of Hc2 and ?(0) 175
7.4.2 Estimation of the Filamentary Diameter 176
7.4.3 Mechanism for Reentrant Superconductivity in Na2-?Mo6Se6 177
7.4.4 Calculations of the Josephson Energy 178
7.4.5 Correspondence Between Experimental Data and Calculations 183
7.5 Concluding Remarks 186
References 187
8 Summary and Outlook 190
8.1 Summary 190
8.1.1 Project Challenges 192
8.2 Outlook 193