Title Topological Insulators
Subtitle
Author Panagiotis Kotetes
ISBN 9781681745169
List price USD 79.95
Price outside India Available on Request
Original price
Binding Paperback
No of pages 216
Book size 178 x 254 mm
Publishing year 2019
Original publisher Morgan & Claypool Publishers (Eurospan Group)
Published in India by .
Exclusive distributors Viva Books Private Limited
Sales territory India, Sri Lanka, Bangladesh, Pakistan, Nepal, .
Status New Arrival
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Description:

This book provides an introduction to topological matter with a focus on insulating bulk systems. A number of prerequisite concepts and tools are first laid out, including the notion of symmetry transformations, the band theory of semiconductors and aspects of electronic transport. The main part of the book discusses realistic models for both time-reversal-preserving and -violating topological insulators, as well as their characteristic responses to external perturbations. Special emphasis is given to the study of the anomalous electric, thermal, and thermoelectric transport properties, the theory of orbital magnetisation, and the polar Kerr effect. The topological models studied throughout this book become unified and generalised by means of the tenfold topological-classification framework and the respective systematic construction of topological invariants. This approach is further extended to topological superconductors and topological semimetals. This book covers a wide range of topics and aims at the transparent presentation of the technical aspects involved. For this purpose, homework problems are also provided in dedicated Hands-on sections. Given its structure and the required background level of the reader, this book is particularly recommended for graduate students or researchers who are new to the field.


Contents:

Preface

Acknowledgements

Author biography

Symbols to topological insulators

Chapter 1. Symmetries and effective Hamiltonians • Crash course on symmetry transformations • Unitary symmetry transformations • Action of symmetry transformations on operators • Antiunitary symmetry transformations: time reversal • Symmetry groups • Translations, Bloch’s theorem and space groups • Effective Hamiltonians for bulk III—V semiconductors • Effective Hamiltonian about the ?-point: plain vanilla model • Cubic crystalline effects and double covering groups • Bulk inversion asymmetry • Confinement and structural inversion asymmetry • Hands-on: symmetry analysis of a triple quantum dot • References

Chapter 2. Electron-coupling to external fields and transport theory • Electromagnetic potentials, fields and currents • Minimal coupling and electric charge conservation law • Charge current in lattice systems • Linear response and current—current correlation functions • Matsubara technique and thermal Green functions • Matsubara formulation of linear response • Charge conductivity of an electron gas • Thermoelectric and thermal transport • Energy conservation and heat current • Luttinger’s gravitational field approach • Nature of the gravitational field • Hands-on: magnetoconductivity tensor of a triangular triple quantum dot • Hands-on: Boltzmann transport equation • References

Chapter 3. Jackiw—Rebbi model and Goldstone—Wilezek formula • Helical electrons in nanowires: emergent Jackiw–Rebbi model • Zero-energy solutions in the Jackiw–Rebbi model • The Jackiw–Rebbi model in condensed matter physics • Polyacetylene and the Su–Schrieffer–Heeger model • One-dimensional conductors and sliding charge density waves • Goldstone–Wilczek formula and dissipationless current • Connection to Dirac physics and chiral anomaly • Fractional electric charge at solitons and electric charge pumping    Hands-on: derivation of the Goldstone–Wilczek formula for a sliding • charge density wave conductor • References

Chapter 4. Topological insulators in 1+1 dimensions • Prototypical topological-insulator model in 1+1 dimensions • Hamiltonian and zero-energy edge states • Topological invariant • Homotopy mapping and winding number • Topological invariance • Generalised winding number • Lattice topological-insulator model and higher winding numbers • Adiabatic transport: Thouless pump and Berry curvature • Continuum model • Relation between Chern and winding numbers • Lattice model and electric polarisation • Berry phase • Hands-on: winding number in a 3+1d model • Hands-on: current and electric polarisation formula • Hands-on: violation of chiral symmetry and electric polarisation • References

Chapter 5. Chern insulators—fundamentals • Jackiw–Rebbi model and Dirac physics in 2 + 1d • Electric charge and current responses of the chiral edge modes • Chiral edge modes in the quantum Hall effect: Laughlin’s argument • Connection to Dirac physics and parity anomaly • Maxwell-Chem-Simons action and topological Meissner effect • Chern insulator in 2 + 1d • Continuum model • Lattice model • Quantised Hall conductance and Chern number—bulk approach • Bulk eigenstates • Adiabatic Hall transport and Berry curvature • Homotopy mapping and Chern number • Chern insulators in higher dimensions • Chern-insulator model in 4 + 1d • Second Chern number and non-Abelian Berry gauge potentials • 4 + 1d Chern-Simons action and four-dimensional quantum  Hall effect • Generalisation to arbitrary dimensions • Dimensional reduction: chiral anomaly • Hands-on: Chern-Simons action • Hands-on: Chern number for interacting systems • Hands-on: second Chern number • References

Chapter 6. Chern insulators—applications • Dynamical anomalous Hall response and polar Kerr effect • Dynamical anomalous Hall conductivity    Polar Kerr effect • Dielectric tensor and circular-polarisation birefringence • Kerr-angle formula • Polar Kerr effect in a 2 + 1d Chern insulator • Chern insulators in an external magnetic field • High-field limit and the formation of Landau levels • Theory of orbital magnetisation—a Green-function method • Anomalous thermoelectric and thermal Hall transport • Thermoelectric conductivity tensor • Thermal conductivity tensor • Diathermal contributions to the conductivities and transport • current    Hands-on: magnetic-field-induced Chern systems • Hands-on: thermoelectric transport in the Haldane model • References

Chapter 7. Z2 topological insulatorsZ2 topological insulators in 2 + 1 dimensions • Bottom-up construction based on Chern insulators: BHZ model • Violation of chiral symmetry and Z2 topological invariant • Z2 topological insulators in 3 + 1 dimensions • Crystal structure and model Hamiltonian • Surface states for negligible warping • Consequences of warping and ? Berry phase • Magnetoelectric polarisation and Z2 topological invariants in 3 + 1d • Dimensional reduction from a 4 + 1d Chern insulator and magnetoelectric coupling  • Dimensional reduction • Magnetoelectric polarisation domain wall and quantum anomalous Hall effect • Hands-on: quasiparticle interference on the topological surface • Hands-on: topological Kondo insulator • References

Chapter 8. Topological classification of insulators and beyond • Generalised antinunitary symmetries and symmetry classes • The art of topological classification • Complex symmetry classes • Real symmetry classes • Z2 classification and relative Chem and winding numbers • Weak topological invariants and flat bands • Topological classification with unitary symmetries • Crystalline topological insulators • Topological classification of gapless systems • 2 + l d semimetals—graphene • Weyl semimetals • Topological classification of insulators and defects • Topological superconductors and Majorana fermions • Further topics and outlook • Hands-on: Berry magnetic monopoles in hole-like semiconductors • Hands-on: Floquet topological insulator • References

Index


About the Author:

Dr Panagiotis Kotetes recently embarked on his five-year faculty appointment at the Institute of Theoretical Physics of the Chinese Academy of Sciences in Beijing. During 2015-2018 he was a postdoctoral researcher at the Niels Bohr Institute of the University of Copenhagen, where this book was mainly written. His first postdoctoral appointment was at the Karlsruhe Institute of Technology, where he worked for five years. Panagiotis carried out his Diploma, Masters and PhD studies at the National Technical University of Athens in Greece. His research interests and activity cover the topics of topological systems, unconventional superconductivity, exotic magnetism, and quantum computing.


Target Audience:

This book is particularly recommended for graduate students or researchers who are new to the field of topological matter. Useful for people interested in materials science and physics.

 

 
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