Chiral $p\pm ip$ superfluid on a sphere

TL;DR

This paper studies a spinless $p ext{-}ip$ superfluid on a sphere, revealing that its ground state must have topological defects and identifying chiral fermion modes localized on these defects.

Contribution

It demonstrates that a $p ext{-}ip$ superfluid on a sphere necessarily contains topological defects and characterizes the localized chiral fermion modes.

Findings

Ground state exhibits topological defects such as vortices or domain walls.

Chiral fermion modes are localized on topological defects.

Spectrum of localized modes is computed.

Abstract

We consider a spinless fermionic $p\pm ip$ superfluid living on a two-dimensional sphere. Using superfluid hydrodynamics we show that the ground state necessarily exhibits topological defects: either a pair of elementary vortices or a domain wall between $p\pm ip$ phases. In the topologically nontrivial BCS phase we identify the chiral fermion modes localized on the topological defects and compute their low-energy spectrum.