Phase diagram of exotic superfluidity of trapped Fermi gases in the 1D-3D crossover: a real-space dynamical mean-field study

Abstract

We present zero and finite temperature phase diagrams of attractively interacting Fermi gases in the dimensional crossover between one and three dimensional lattices [1,2]. The elusive Fulde- Ferrell-Larkin-Ovchinnikov (FFLO) state has been anticipated to be possibly the best visible in the 1D-3D crossover regime with the long-range order supported by the increased dimensionality. With an explicit trap potential considered within the real-space dynamical mean-field theory, here we show how thermal fluctuations and increased intermediate dimensionality play together to build and stabilize the shell structure of the FFLO phase along the trap. We find that at zero temperature, the FFLO state characterizes a significantly large area of the phase diagram throughout the dimensional crossover regime. Remarkably at finite temperatures, we find that the critical temperature of the FFLO phase is about one third of the BCS critical temperature of the spin-population balanced counterpart, regardless of the intermediate dimensionality examined. With increasing temperature, we also characterize the dimension-sensitive melting of the FFLO shell structure along the trap, extending the picture of the zero-temperature shell structure evolution along the dimensional crossover to the comprehensive finite-temperature regime.