Vortex lattice of Fermi superfluid on a sphere

In planar geometry, superconductors and superfluids can form vortex lattices to minimize the ground-state energy in the presence of magnetic flux or rotation. We generalize the vortex lattices of Fermi superfluids to curved geometries exemplified by the spherical surface using the Ginzburg-Landau theory. As an analogue to the perpendicular magnetic flux in the planar case, radial magnetic flux from a magnetic monopole source is introduced, presumably through artificial gauge field induced by light-matter interactions of cold atoms in a spherical-shell geometry. Since there is no regular lattice on a sphere beyond 20 vertices, the planar construction using translational operations does not apply to the spherical case. We instead represent the lowest Landau-level states by monopole spherical harmonics and use the random, Fibonacci, and geodesic-dome lattices as scaffolds to construct the vortex lattice solutions. At each vortex, a circulating supercurrent and quantized winding number are confirmed. We also found that the geodesic-dome lattice (Fibonacci lattice) has the lowest energy when the number of vortices are small (large).