Non-Abelian Statistics of Half-Quantum Vortices in $\mathit{p}$-Wave Superconductors

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.