Topology in Condensed Matter

F. D. M. Haldane

Saurabh Basu

Jesús Giménez Urrea

Shun-Qing Shen

Abstract The discovery of topological insulators and superconductors is an important advance in condensed matter physics. Topological phases reflect global properties of the quantum states in materials, and the boundary states are the characteristic of the materials. Such phases constitute a new branch in condensed matter physics. Here a historic development is briefly introduced, and the known family of phases in condensed matter are summarized.

M. A. N. Araújo, Pedro D Sacramento

Topology in Condensed MatterT his text serves as a pedagogical introduction to the theoretical concepts on application of topology in condensed matter systems.It covers an introduction to basic concepts of topology, emphasizes the relation of geometric concepts such as the Berry phase to topology, having in mind applications in condensed matter.In addition to describing two basic systems such as topological insulators and topological superconductors, it also reviews topological spin systems and photonic systems.It also describes the use of quantum information concepts in the context of topological phases and phase transitions, and the effect of non-equilibrium perturbations on topological systems.This book provides a comprehensive introduction to topological insulators, topological superconductors and topological semimetals.It includes all the mathematical background required for the subject.There are very few books with such a coverage in the market.

M. A. N. Araújo, Pedro D Sacramento

This text serves as a pedagogical introduction to the theoretical concepts on application of topology in condensed matter systems. It covers an introduction to basic concepts of topology, emphasizes the relation of geometric concepts such as the Berry phase to topology, having in mind applications in condensed matter. In addition to describing two basic systems such as topological insulators and topological superconductors, it also reviews topological spin systems and photonic systems. It also describes the use of quantum information concepts in the context of topological phases and phase transitions, and the effect of non-equilibrium perturbations on topological systems. This book provides a comprehensive introduction to topological insulators, topological superconductors and topological semimetals. It includes all the mathematical background required for the subject. There are very few books with such a coverage in the market.