A Brief Introduction to Topology and Differential Geometry in Condensed Matter Physics (Second Edition)

Concepts drawn from topology and differential geometry have become essential to the understanding of several phenomena in condensed matter physics. This book provides a self-consistent introduction to the mathematical ideas and methods from these fields that will enable the student of condensed matter physics to begin applying these concepts with confidence. This expanded second edition adds eight new chapters, including one on the classification of topological states of topological insulators and superconductors and another on Weyl semimetals, as well as elaborated discussions of the Aharonov-Casher effect, topological magnon insulators, topological superconductors and K-theory.

Key Features:

• Provides an introduction to path integral formalism

• Introduces all the basic concepts in differential geometry and topology

• Presents the quantum Hall effect using topology concepts

• Includes an introduction to topological insulators

• Presents the Weyl semimetal using topological concepts

• Studies spin systems using topology

Antonio Sergio Teixeira Pires graduated from University of California in Santa Barbara in 1976. He is a professor of Physics at Universidade Federal de Minas Gerais, Brazil doing research in the area of magnetism. He is a member of the Brazilian Academy of Science. He was the Editor of the Brazilian Journal of Physics and a member of the Advisory Board of the Journal of Condensed Matter Physics. He has published 230 papers and the books 'Theoretical tools for spin models in Magnetic systems', 'ADS/CFT correspondence in Condensed Matter' and 'A brief introduction to topology and differential geometry in condensed matter physics' in the IOP Publishing eBooks and Concise series.