Approximate vortex lattices of atomic Fermi superfluid on a spherical surface

TL;DR

This paper investigates approximate vortex lattice structures in atomic Fermi superfluids on spherical surfaces, using geometric and numerical methods, with implications for ultracold atom experiments.

Contribution

It introduces two novel methods to construct and analyze vortex structures on spherical geometries, extending the understanding of superfluid vortex arrangements beyond planar systems.

Findings

Vortices are confirmed as zeros of the order parameter with circulating currents.

Both constructions' Abrikosov parameters approach the planar value as vortex number increases.

The methods provide insights relevant for ultracold atoms in spherical-shell geometries.

Abstract

While planar Fermi superfluids form Abrikosov vortex lattices under magnetic or effective gauge fields, spherical geometry forbids perfect lattices above 20 vortices. We characterize approximate vortex structures of atomic Fermi superfluids under an effective monopole field on a spherical surface as an analogue of the planar vortex-lattice problem by two constructions based on the Ginzburg-Landau theory. The first one is geometric and uses the random, geodesic-dome, and Fibonacci lattices as scaffolds to construct the order parameter from the degenerate monopole harmonics. The second one minimizes the free energy by numerically adjusting the coefficients to find the solution with the minimal Abrikosov parameter. We have verified the vortices from both constructions are zeros of the order parameter with circulating currents around the vortex cores. As the number of vortices increases, the Abrikosov parameters of both the Fibonacci-lattice and minimization solutions extrapolate to the planar value. We briefly discuss implications for ultracold atoms in thin spherical-shell geometry.