Larkin-Ovchinnikov-Fulde-Ferrell state of spin polarized atomic Fermi superfluid on a spherical surface

TL;DR

This paper investigates the LOFF state in a spin-polarized atomic Fermi superfluid confined on a spherical surface using the BdG formalism, revealing the conditions for its stability and spatial characteristics.

Contribution

It introduces a phase diagram for LOFF states on a spherical surface and compares their stability to uniform solutions, highlighting the fragility of the LOFF state.

Findings

LOFF states with multiple nodes are more stable at higher spin polarization.

LOFF states only exist near the phase boundary where uniform solutions vanish.

The LOFF state is fragile and sensitive to the boundary conditions on a spherical surface.

Abstract

By implementing the Bogoliubov-de Gennes (BdG) formalism of population-imbalanced atomic Fermi gases with pairing interactions in a thin spherical shell, we characterize the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state in such a compact geometry. We first construct a phase diagram showing where uniform solutions of spin-polarized Fermi superfluid from the BdG equation cease to exist due to the vanishing order parameter. Near the boundary, various LOFF states with spatially modulating order parameters and density profiles can survive as convergent solutions to the BdG equation. When both uniform and LOFF solutions are present, we compare their grand potentials to determine the energetically favorable state and find that the LOFF states with multiple nodes in the order parameter become more stable at higher spin polarization. However, the LOFF state only survives close to the phase boundary where the uniform solutions vanish, indicating fragility of the LOFF state on a spherical surface. We also briefly discuss possible implications.