Topological Quantum Materials: Concepts, Models, and Phenomena

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