This book offers a primer on the fundamental theory of Andreev reflection, a fundamental process in the motion of a Cooper pair, which dominates low-energy electronic transport properties in superconductor junctions including differential conductance and Josephson current. The book concisely describes how Andreev reflection impacts the low-energy physics of electronic transport especially in topologically non-trivial superconductor junctions. In addition, it includes an introduction to topological superconductors, covering topological classification, chiral and helical superconductors, and topological edges.

The book is based on the author's lecture notes, used in his intensive lectures and while supervising his upper undergraduate and early graduate students. To fully benefit from this concise primer, readers only need an undergraduate background in quantum mechanics and statistical mechanics. Further, by highlighting Josephson junctions of topological superconductors, thebook offers readers a glimpse into cutting-edge topics.

Autorentext

Yasuhiro Asano is an associate professor at the Department of Applied Physics, Hokkaido University. His work mainly involves quantum transport theory of unconventional superconductors. He received his Ph. D. from Nagoya University in 1995. After serving as a postdoctoral fellow at Delft University of Technology, he joined Hokkaido University as a research associate at the Department of Applied Physics in 1995, and became a lecturer in 2008. He has served in the current position since 2011.

Inhalt

Chapter 1: Introduction

1.1 Scope of this Book

1.2 Overview of Superconducting Phenomena

Chapter 2: Theoretical tool

2.1 Harmonic Oscillator

2.2 Free Electrons in a Metal

2.3 Coherent State

Chapter 3: Mean-field theory of superconductivity

3.1 Pairing Hamiltonian

3.2 Mean-Field Approximation

3.3 Gap Equation and Thermodynamic Properties

3.4 Cooper Pair

3.5 Magnetic Properties

Chapter 4: Andreev reflection

4.1 Conductance in an NS Junction

4.2 Retroreflectivity

4.3 Josephson Current in an SIS Junction

Chapter 5: Unconventional superconductors

5.1 Conductance in a NS Junction

5.2 Surface Andreev Bound States

5.3 Josephson Current in an SIS Junction

5.4 Andreev Bound States in an SIS Junction

5.5 Topological Classification

Chapter 6: Various Josephson junctions

6.1 Singlet-Singlet Junction

6.2 Triplet-Triplet Junction

6.3 Singlet-Triplet Junction

6.4 Chiral Superconductor

6.5 Helical Superconductor

Chapter 7: Proximity Effect

7.1 A Cooper Pair in a Clean Metal

7.2 Andreev Reflection and Diffusive Motion

7.3 Anomalous Proximity Effect