Exotic Paired states of Ultracold fermi gases in 1d-3d dimensional crossover

Abstract

One of fundamental questions in condensed matter physics is what would happen in super- conductivity if the symmetric setting of the BCS theory is broken. The asymmetrical pairing scenarios beyond the standard BCS pairing mechanism have been suggested with the imposed Fermi surface mismatch, causing, for instance, the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) or Sarma/breach-pair states. However, these exotic paired states remain essentially elusive so far despite of indirect experimental evidences in heavy-fermion superconductors and ultracold atomic gases. Here, we present the phase diagrams of the 1D-3D dimensional crossover in lattices both at zero temperature and finite temperatures by employing the real-space dynamical mean-field theory incorporating with the exact diagonalization and quantum Monte Carlo methods. In the zero- and finite-temperature phase diagrams [1,2], we find that the dimensionality can strongly af- fect the shell structure that undergoes a crossover between distinctive quasi-1D and quasi-3D shell structures with corresponding dimensionality-dependent FFLO states. Both at zero and finite temperatures, we predict an optimal regime for the FFLO state that is considerably extended to intermediate dimensions and mid-range polarizations. While the meting characteristics of FFLO state strongly depend on the dimensionality, we find that the critical temperature of the FFLO state is considerably high at intermediate dimensions, one third of the BCS critical temperature of the spin-population balanced counterpart.