OneDimensional Superconductivity in Nanowires -- Contents -- Preface -- Abbreviations and Symbols -- Color Plates -- Part One Theoretical Aspects of Superconductivity in 1D Nanowires -- 1 Superconductivity: Basics and Formulation -- 1.1 Introduction -- 1.2 BCS Theory -- 1.3 Bogoliubov-de Gennes Equations - Quasiparticle Excitations -- 1.4 Ginzburg-Landau Theory -- 1.4.1 Time-Dependent Ginzburg-Landau Theory -- 1.5 Gorkov Green's Functions, Eilenberger-Larkin-Ovchinnikov Equations, and the Usadel Equation -- 1.6 Path Integral Formulation -- References -- 2 1D Superconductivity: Basic Notions -- 2.1 Introduction -- 2.2 Shape Resonances - Oscillations in Superconductivity Properties -- 2.2.1 Early Treatments of Shape Resonances in 2D Films -- 2.2.2 Bogoliubov-de Gennes Equations, Finite Temperature, and Parabolic-Band Approximation for Realistic Materials -- 2.2.3 Numerical Solutions and Thin Film Shape Resonances -- 2.2.4 1D Nanowires - Shape Resonances and Size Oscillations -- 2.3 Superconductivity in Carbon Nanotubes - Single-Walled Bundles and Individual Multiwalled Nanotubes -- 2.4 Phase Slips -- 2.4.1 Finite Voltage in a Superconducting Wire and Phase Slip -- 2.4.2 Phase Slip in a Josephson Junction -- 2.4.3 Langer-Ambegaokar Free Energy Minima in the Ginzburg-Landau Approximation -- 2.4.4 Transition Rate and Free Energy Barrier -- 2.4.5 Free Energy Barrier for a Phase Slip in the Ginzburg-Landau Theory -- 2.4.6 Physical Scenario of a Thermally-Activated Phase Slip -- 2.4.7 McCumber-Halperin Estimate of the Attempt Frequency -- References -- 3 Quantum Phase Slips and Quantum Phase Transitions -- 3.1 Introduction -- 3.2 Zaikin-Golubev Theory -- 3.2.1 Derivation of the Low Energy Effective Action -- 3.2.2 Core Contribution to the QPS Action -- 3.2.3 Hydrodynamic Contribution to the Phase-Slip Action -- 3.2.4 Quantum Phase-Slip Rate.

3.2.5 Quantum Phase-Slip Interaction and Quantum-Phase Transitions -- 3.2.6 Wire Resistance and Nonlinear Voltage-Current Relations -- 3.3 Short-Wire Superconductor-Insulator Transition: Büchler, Geshkenbein and Blatter Theory -- 3.4 Refael, Demler, Oreg, Fisher Theory - 1D Josephson Junction Chains and Nanowires -- 3.4.1 Discrete Model of 1D Josephson Junction Chains -- 3.4.2 Resistance of the Josephson Junctions and the Nanowire -- 3.4.3 Mean Field Theory of the Short-Wire SIT -- 3.5 Khlebnikov-Pryadko Theory - Momentum Conservation -- 3.5.1 Gross-Pitaevskii Model and Quantum Phase Slips -- 3.5.2 Disorder Averaging, Quantum Phase Transition and Scaling for the Resistance and Current-Voltage Relations -- 3.5.3 Short Wires - Linear QPS Interaction and Exponential QPS Rate -- 3.6 Quantum Criticality and Pair-Breaking - Universal Conductance and Thermal Transport in Short Wires -- References -- 4 Duality -- 4.1 Introduction -- 4.2 Mooij-Nazarov Theory of Duality - QPS Junctions -- 4.2.1 QPS Junction Voltage-Charge Relationship and Shapiro Current Steps -- 4.2.2 QPS Qubits -- 4.3 Khlebnikov Theory of Interacting Phase Slips in Short Wires: Quark Confinement Physics -- References -- 5 Proximity Related Phenomena -- 5.1 Introduction -- 5.2 Transport Properties of Normal-Superconducting Nanowire-Normal (N-SCNW-N) Junctions -- 5.2.1 Nonequilibrium Usadel Equations -- 5.2.2 Parameterization of the Usadel Equations -- 5.2.3 Numerical Results -- 5.3 Superconductor-Semiconductor Nanowire-Superconductor Junctions -- 5.4 Majorana Fermion in S-SmNW-S Systems with Strong Spin-Orbit Interaction in the Semiconductor -- References -- Part Two Review of Experiments on 1D Superconductivity -- 6 Experimental Technique for Nanowire Fabrication -- 6.1 Experimental Technique for the Fabrication of Ultra Narrow Nanowires -- 6.2 Introduction to the Techniques.

6.2.1 Lithography -- 6.2.2 Metal Deposition -- 6.2.3 Etching -- 6.2.4 Putting It All Together -- 6.3 Step-Edge Lithographic Technique -- 6.4 Molecular Templating -- 6.5 Semiconducting Stencils -- 6.6 Natelson and Willet -- 6.7 SNAP Technique -- 6.8 Chang and Altomare -- 6.9 Template Synthesis -- 6.10 Other Methods -- 6.10.1 Ion Beam Polishing -- 6.10.2 Angled Evaporation -- 6.10.3 Resist Development -- 6.11 Future Developments -- References -- 7 Experimental Review of Experiments on 1D Superconducting Nanowires -- 7.1 Introduction -- 7.2 Filtering -- 7.3 Phase Slips -- 7.4 Overview of the Experimental Results -- 7.4.1 Giordano's Experiments -- 7.4.2 Recent Experiments on QPS -- 7.4.3 QPS Probed via Switching Current Measurements -- 7.5 Other Effects in 1D Superconducting Nanowires -- 7.5.1 S-Shaped Current-Voltage Characteristic -- 7.6 Antiproximity Effect -- 7.6.1 Stabilization of Superconductivity by a Magnetic Field -- 7.6.2 Shape Resonance Effects -- References -- 8 Coherent Quantum Phase Slips -- 8.1 Introduction -- 8.2 A Single-Charge Transistor Based on the Charge-Phase Duality of a Superconducting Nanowire Circuit -- 8.3 Quantum Phase-Slip Phenomenon in Ultranarrow Superconducting Nanorings -- 8.4 Coherent Quantum Phase Slip -- 8.5 Conclusion -- References -- 9 1D Superconductivity in a Related System -- 9.1 Introduction -- 9.2 Carbon Nanotubes -- 9.2.1 Proximity Effects in SWNT -- 9.2.2 Intrinsic Superconductivity in SWNT -- 9.2.3 Superconductivity in Ropes Mediated by the Environment -- 9.3 Majorana Experiments -- 9.3.1 Majorana Experiment in Semiconducting Nanowires -- 9.3.2 Majorana Experiment in Hybrid Superconductor-Topological Insulator Devices -- 9.4 Superconducting Nanowires as Single-Photon Detectors -- References -- 10 Concluding Remarks -- Index.