Majorana Fermions and Topology in Superconductors

TL;DR

This paper reviews topological superconductors, focusing on Majorana fermions, their stability, unique quantum statistics, and potential applications in quantum computing, along with interaction effects and Weyl superconductors.

Contribution

It provides a comprehensive pedagogical overview of Majorana fermions in topological superconductors, including their properties, stability, and implications for quantum computation.

Findings

Majorana fermions appear as Bogoliubov quasiparticles in topological superconductors.

Majorana fermions obey non-Abelian statistics, enabling topological quantum computation.

Interaction effects influence the topological classification of superconductors.

Abstract

Topological superconductors are novel classes of quantum condensed phases, characterized by topologically nontrivial structures of Cooper pairing states. On the surfaces of samples and in vortex cores of topological superconductors, Majorana fermions, which are particles identified with their own anti-particles, appear as Bogoliubov quasiparticles. The existence and stability of Majorana fermions are ensured by bulk topological invariants constrained by the symmetries of the systems. Majorana fermions in topological superconductors obey a new type of quantum statistics referred to as non-Abelian statistics, which is distinct from bose and fermi statistics, and can be utilized for application to topological quantum computation. Also, Majorana fermions give rise to various exotic phenomena such as "fractionalization", non-local correlation, and "teleportation". A pedagogical review of these subjects is presented. We also discuss interaction effects on topological classification of superconductors, and the basic properties of Weyl superconductors.