Non-abelian statistics of half-quantum vortices in p-wave superconductors

TL;DR

From the properties of the solutions to Bogoliubov-de Gennes equations in the vortex core, the non-Abelian statistics of vortices are derived identical to that for the Moore-Read (Pfaffian) quantum Hall state.

Abstract

Excitation spectrum of a half-quantum vortex in a p-wave superconductor contains a zero-energy Majorana fermion. This results in a degeneracy of the ground state of the system of several vortices. From the properties of the solutions to Bogoliubov-de-Gennes equations in the vortex core we derive the non-abelian statistics of vortices identical to that for the Moore-Read (Pfaffian) quantum Hall state.

Figures (3)

• Figure 1: Half-quantum vortex. Arrows denote the direction of vector ${\bf \hat{d}}$.
• Figure 2: Defining relation for the braid group: $T_i T_{i+1} T_i = T_{i+1} T_i T_{i+1}$.
• Figure 3: Elementary braid interchange of two vortices.