Topological Quantum Materials: Concepts, Models, and Phenomena

✍ Scribed by Grigory Tkachov

• Publisher: CRC Press
• Year: 2022
• Tongue: English
• Leaves: 288
• Category: Library

✦ Synopsis

In topological quantum materials, quantum effects emerge at macroscopic scales and are robust to continuous changes in a material’s state. This striking synergy between quantum and topological properties is of great interest for both fundamental research and emerging technologies, especially in the fields of electronics and quantum information. This edition of the book presents a wealth of topological quantum materials, bringing together burgeoning research from different areas: topological insulators, transition metal dichalcogenides, Weyl semimetals, and unconventional and topological superconductors. The realization of the application potential of topological quantum materials requires understanding their properties at a fundamental level. This brings us back to the discovery of topological phases of matter, which earned the Nobel Prize in Physics in 2016. This book explores the connection between pioneering work on topological phases of matter and a flurry of activity that followed. The topics covered include the quantum anomalous and spin Hall effects, emergent axion electrodynamics and topological magnetoelectric effects, Weyl nodes and surface Fermi arcs, weak antilocalization, induced triplet superconductivity, Majorana fermion modes, and the fractional Josephson effect.

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Chapter 1: Introducing Topological Materials: Mind the Time Reversal
1.1: Time-Reversal Symmetry, Antiunitary T Operation and Kramers’ Theorem
1.2: Broken Time-Reversal Symmetry, Chiral Edge States and Quantum Hall Effect
1.3: From Chiral to Helical: Quantum Spin Hall Insulators
1.4: Graphene, Related 2D Materials, Inverted Semiconductors and 1T' Transition Metal Dichalcogenides
1.5: Quantum Anomalous Hall Insulators
1.6: Three-Dimensional Topological Insulators
1.7: Weyl Semimetals
1.8: Topological Superconductors
Chapter 2: Two-Dimensional Topological Insulators
2.1: Chern Insulators I
2.1.1: Edge Mode and Band Inversion
2.1.2: Berry’s Phase and Curvature
2.1.3: Thouless–Kohmoto–Nightingale–den Nijs Formula for the Hall Conductivity. Topological Invariants
2.2: Quantum Spin Hall Insulators I
2.2.1: Dirac Model
2.2.2: Bulk Band Structure
2.2.3: Edge States. Spin Helicity
2.3: Chern Insulators II
2.3.1: Tight-Binding Model on a Square Lattice
2.3.2: Normal and Inverted Band Structure. Chern Number and Edge Mode
2.4: Quantum Spin Hall Insulators II
2.4.1: Tight-Binding, Bernevig–Hughes–Zhang and Related Models
2.4.2: Z2 Invariant and Helical Edge States
2.4.3: Nonlocal Edge Transport
2.5: Towards Room-Temperature Quantum Spin Hall Insulators: 2D Transition Metal Dichalcogenides
2.5.1: Monolayer Transition Metal Dichalcogenides as Quantum Spin Hall Insulators
2.5.2: Effective Model for 1T' - TMDs
2.5.3: 1T' - 1H Phase Interface and Boundary States
2.5.4: Boundary Conductance and Thermopower
2.6: Problems
Chapter 3: Two-Dimensional Topological Insulatorswith Broken Time-Reversal Symmetry
3.1: Quantum Anomalous Hall Insulators I
3.1.1: Dirac Model
3.1.2: Phase Classification by TKNN Invariant
3.1.3: Phase Classification by Edge States
3.2: Quantum Anomalous Hall Insulators II
3.2.1: Tight-Binding and Bernevig–Hughes–Zhang Models
3.2.2: Phase Classification by TKNN Invariant
3.2.3: Phase Classification by Edge States
3.3: Quantum Spin Hall Insulators under an Orbital Magnetic Field Effect
3.3.1 Boundary Problem. Green’s Function Method
3.3.2: Solution in Terms of Parabolic Cylinder Functions
3.3.3: Nonlinear Helical Spectrum
3.3.4: Spatial Distribution of Edge States
3.4: Backscattering, Conductance and Topological Transitions
3.4.1: Free Edge-State Propagator
3.4.2: Edge Scattering Matrix and Fisher–Lee Relation
3.4.3: Solution of Dyson Equation. Conductance
3.4.4: Transition from 2DTI to a Quantum Hall State
3.5: Problems
Chapter 4: Three-Dimensional Topological Insulators and Weyl Semimetals
4.1: Strained HgTe as a 3DTI. Helical Surface States
4.1.1: Kane’s Hamiltonian and Boundary Conditions
4.1.2: Surface-State Dispersion, Helicity and Decay Length
4.2: Bi-Based 3DTIs and Thin TI Materials
4.2.1: Surface States in Bi2Se3 and Bi2Te3
4.2.2: TI Thin Films
4.3: Weyl Semimetals
4.3.1: “Diabolical” Points in 3D k-Space
4.3.2: Tight-Binding Model on a Cubic Lattice. Weyl Nodes
4.3.3: Chern Numbers
4.3.4: Fermi Arcs
4.3.5: Spin–Orbit Split Weyl Semimetal
4.4: Problems
Chapter 5: Surface Electron Transport and Magneto-Optics
5.1: Electron Transport in Disordered TI Materials: Phenomenology
5.1.1: Diffusion and Spin-Momentum Locking
5.1.2: Weak Localization and Antilocalization
5.2: Weak Antilocalization in TI Thin Films
5.2.1: Kubo Formula: Green’s Functions
5.2.2: Potential Disorder
5.2.3: Nonperturbative Treatment of Disorder: Diagrammatics
5.2.4: Cooperon
5.2.5: Cooperon for a Conventional Metal
5.2.6: Cooperon for a Helical Metal
5.2.7: Quantum Conductivity Correction
5.2.8: Conductivity Correction for a Conventional Metal
5.2.9: Conductivity Correction for a Helical Metal
5.3: Weak Antilocalization on TI Surfaces
5.3.1: Scattering Times
5.3.2: Cooperon
5.3.3: Quantum Conductivity Correction
5.3.4: Magnetoconductivity
5.4: Quantum Hall Effect on TI Surfaces
5.4.1: Recalling Landau Levels of a Rashba 2DES
5.4.2: Landau Quantization of Surface States: Half-Integer-Quantized Hall Conductivity
5.4.3: AC Conductivities: Cyclotron Resonance
5.5: Emergent Axion Electrodynamics and Topological Magnetoelectric Effect
5.5.1: Emergent Axion Field: Modified Maxwell’s Equations
5.5.2: Quantized Faraday Rotation due to Topological Magnetoelectric Effect
5.6: Problems
Chapter 6: Unconventional Designer Superconductors
6.1: Introduction to Superconductivity
6.1.1: Electron–Electron Pairing: Mean-Field Theory
6.1.2: Nambu Representation
6.1.3: Bogoliubov–de Gennes equation: Particle-Hole Symmetry
6.2: Induced Mixed-Parity Superconductivity in TIs
6.2.1: Classification of Superconducting Pairing: Mixed-Parity Order Parameter
6.2.2: Theory of the Mixed-Parity Proximity Effect
6.2.3: Helical Andreev Bound States
6.2.4: Emergent Majorana Fermions
6.2.5: Josephson Effect: Superconducting Klein Tunneling
6.3: Induced Triplet Superconductivity in TIs
6.3.1: Odd-Frequency Triplet Superconductivity
6.3.2: Non-Unitary Triplet Superconductivity: Charge-Spin Conversion
6.4: Problems
Chapter 7: Topological Superconductors and Majorana Modes
7.1: Chiral Superconductors: Majorana Edge Modes
7.1.1: Topological px + ipy Superconductivity: Phenomenology
7.1.2: Topological px + ipy Superconductivity in Hybrid QAHI Structures
7.2: Topological Josephson Junctions
7.2.1: Majorana Zero Modes and Ground State Degeneracy
7.2.2: Majorana Zero Modes in a px Superconductor
7.2.3: Majorana Zero Modes in a QSHI Channel
7.2.4: Fractional Josephson Effect
7.3: Non-Abelian Exchange Statistics and Braiding
7.4: Problems
Appendix A: Weak Antilocalization in Topological Insulators
Appendix B: Unconventional Superconductivity in Noncentrosymmetric Proximity Superconductors
Bibliography
Index