Topological insulators and superconductors

TL;DR

This paper reviews the theoretical models, material properties, and experimental findings of topological insulators and superconductors, highlighting their unique surface states protected by symmetry and their potential for quantum applications.

Contribution

It provides a comprehensive overview of topological insulators and superconductors, including their theoretical frameworks, material realizations, and experimental observations.

Findings

Topological insulators exhibit protected gapless surface states.

Topological superconductors host Majorana fermions on their surfaces.

Experimental evidence supports the existence of these topological phases.

Abstract

Topological insulators are new states of quantum matter which can not be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi$_2$Te$_3$ and Bi$_2$Se$_3$ crystals. We review theoretical models, materials properties and experimental results on two-dimensional and three-dimensional topological insulators, and discuss both the topological band theory and the topological field theory. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. We review the theory of topological superconductors in close analogy to the theory of topological insulators.