Topological Field Theory for p-wave Superconductors

TL;DR

This paper develops a topological field theory for p-wave superconductors featuring Majorana modes, highlighting their topological properties, non-abelian statistics, and potential implications for quantum states and higher-dimensional systems.

Contribution

It introduces a novel topological field theory framework for spinless p-wave superconductors with Majorana modes, connecting to quantum Hall states and extending to spinful and 3D cases.

Findings

Majorana modes are localized at vortex cores and edges.

Ground state degeneracy on a torus confirms non-abelian statistics.

Connection established between p-wave superconductors and Moore-Read state.

Abstract

We propose a topological field theory for a spin-less two-dimensional chiral superconductor that contains fundamental Majorana fields. Due to a fermionic gauge symmetry, the Majorana modes survive as dynamical degrees of freedom only at magnetic vortex cores, and on edges. We argue that these modes have the topological properties pertinent to a p-wave superconductor including the non-abelian braiding statistics, and support this claim by calculating the ground state degeneracy on a torus. We also briefly discuss the connection to the Moore-Read Pfaffian quantum Hall state, and extensions to the spinful case and to three-dimensonal topological superconductors.