© 2012

Topological Insulators

Dirac Equation in Condensed Matters

  • Describes the hot newly discovered materials

  • Presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation

  • A starting point to enter the new research field-topological insulators


Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 174)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Shun-Qing Shen
    Pages 1-11
  3. Shun-Qing Shen
    Pages 13-27
  4. Shun-Qing Shen
    Pages 47-73
  5. Shun-Qing Shen
    Pages 75-84
  6. Shun-Qing Shen
    Pages 85-112
  7. Shun-Qing Shen
    Pages 113-139
  8. Shun-Qing Shen
    Pages 159-172
  9. Shun-Qing Shen
    Pages 173-190
  10. Shun-Qing Shen
    Pages 191-201
  11. Back Matter
    Pages 211-225

About this book


Topological insulators are insulating in the bulk, but process metallic states around its boundary owing to the topological origin of the band structure. The metallic edge or surface states are immune to weak disorder or impurities, and robust against the deformation of the system geometry. This book, Topological insulators, presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation. A series of solutions of the bound states near the boundary are derived, and the existing conditions of these solutions are described. Topological invariants and their applications to a variety of systems from one-dimensional polyacetalene, to two-dimensional quantum spin Hall effect and p-wave superconductors, and three-dimensional topological insulators and superconductors or superfluids are introduced, helping readers to better understand this fascinating new field.

This book is intended for researchers and graduate students working in the field of topological insulators and related areas.

Shun-Qing Shen is a Professor at the Department of Physics, the University of Hong Kong, China.


Marjorana Fermions Modified Dirac Equation Quantum Spin Hall Effect The Dirac Equation The Hall Effect The Surface States Topological Field Theory Topological Insulator Topological Superconductivity

Authors and affiliations

  1. 1., Department of PhysicsThe University of Hong KongHongkongChina, People's Republic

About the authors

Professor Shun-Qing Shen, an expert in the field of condensed matter physics, is distinguished for his research works on spintronics of semiconductors, quantum magnetism and orbital physics in transition metal oxides, and novel quantum states of condensed matters. He proposed the theory of  topological Anderson insulator, spin transverse force, resonant spin Hall effect and the theory of phase separation in colossal magnetoresistive (CMR) materials. He proved the existence of antiferromagnetic long-range order and off-diagonal long-range order in itinerant electron systems.

Professor Shun-Qing Shen has been a professor of physics at The University of Hong Kong since July 2007. Professor Shen received his BS, MS, and PhD in theoretical physics from Fudan University in Shanghai. He was a postdoctorial fellow (1992 – 1995) in China Center of Advanced Science and Technology (CCAST), Beijing, Alexander von Humboldt fellow (1995 – 1997) in Max Planck Institute for Physics of Complex Systems, Dresden, Germany, and JSPS research fellow (1997) in Tokyo Institute of Technology, Japan. In December 1997 he joined Department of Physics, The University of Hong Kong. He was awarded Croucher Senior Research Fellowship (Croucher Prize) in 2010.

Bibliographic information

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From the reviews:

“The book is devoted to the study of a large family of topological insulators and superconductors based on the solutions of the Dirac equation … . this book combines clear physical approaches and strict mathematics. It is very interesting from a methodical viewpoint for teaching the modern physics of condensed matters.” (I. A. Parinov, zbMATH, Vol. 1273, 2013)