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Population imbalanced lattice fermions near the BCS-BEC crossover: II. The FFLO regime and its thermal signatures

We study the effect of high population imbalance in the two dimensional attractive Hubbard model, in the coupling regime corresponding to BCS-BEC crossover, and focus on thermal effects on the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. Using a method that retains all the classical thermal fluctuations on the FFLO state we estimate a very low $T_c$ and infer a strongly first order normal state to FFLO transition. The $T_c$ is an order of magnitude below the mean field estimate. We track the fermionic momentum distribution, the density of states, and the pairing structure factor deep into the normal state. The pairing structure factor retains weak signature of finite momentum pairing to a high temperature despite the low $T_c$ itself, while the spin resolved density of states changes from the `pseudogapped' FFLO character to gapless and pseudogapped again with increasing temperature. These results map out the rather narrow temperature window, and diverse physical indicators, relevant to FFLO states on a cold atom optical lattice, and complements our work on the lower field `breached pair' state.