Curvature Induced Topological Defects of $p$-wave Superfluid on a Sphere

TL;DR

This paper investigates how Gaussian curvature on a sphere induces magnetic fields that lead to topological defects in a $p$-wave superfluid, revealing novel defect structures and phase behavior.

Contribution

It introduces a microscopic model linking curvature to emergent magnetic fields and analyzes the resulting topological defects in the superfluid ground state.

Findings

Gaussian curvature induces a Dirac monopole field on the sphere.

Topological defects include vortices at poles or domain walls.

Phase diagram of the superfluid states is provided.

Abstract

We study the ground state of spinless fermions living on a sphere across $p$-wave Feschbach resonances. By construsting a microscopic model of fermions on a general curved surface, we show that the Guassian curvature induces an emergent magnetic field coupled to the $p\pm ip$ order parameters. In the case of a sphere, the magnetic field corresponds to a Dirac monopole field, which causes topological defects in the superfluid ground state. Using the BCS mean field theory, we calculate its many-body ground state self consistently and give the phase diagram. The ground state may exhibit two types of topological defects, two voritces on the south and north pole or a domain wall which separates $p_\theta+ ip_\phi$ and $p_\theta-ip_\phi$ superfluids.