Exotic paired states with anisotropic spin-dependent Fermi surfaces

TL;DR

This paper proposes a model for cold atomic Fermi gases with anisotropic, spin-dependent Fermi surfaces, revealing exotic superfluid and Bose-metal phases with unique gapless and unpaired excitations.

Contribution

It introduces a novel method to engineer anisotropic Fermi surfaces and predicts new paired states, including a gapless superfluid and a Cooper-pair Bose-Metal phase.

Findings

Existence of a gapless, unpolarized superfluid state with coexisting unpaired carriers.

Prediction of a Cooper-pair Bose-Metal phase with gapless pair excitations on a Bose-surface.

Phase diagram showing transitions as a function of anisotropy, density, and interaction strength.

Abstract

We propose a model for realizing exotic paired states in cold atomic Fermi gases. By using a {\it spin dependent} optical lattice it is possible to engineer spatially anisotropic Fermi surfaces for each hyperfine species, that are rotated 90 degrees with respect to one another. We consider a balanced population of the fermions with an attractive interaction. We explore the BCS mean field phase diagram as a function of the anisotropy, density, and interaction strength, and find the existence of an unusual paired superfluid state with coexisting pockets of momentum space with gapless unpaired carriers. This state is a relative of the Sarma or breached pair states in polarized mixtures, but in our case the Fermi gas is unpolarized. We also propose the possible existence of an exotic paired "Cooper-pair Bose-Metal" (CPBM) phase, which has a gap for single fermion excitations but gapless and uncondensed "Cooper pair" excitations residing on a "Bose-surface" in momentum space.