Thermal transitions, pseudogap behavior and BCS-BEC crossover in Fermi-Fermi mixtures.

We study the mass imbalanced Fermi-Fermi mixture within the framework of a two-dimensional lattice fermion model. Based on the thermodynamic and species dependent quasiparticle behavior we map out the finite temperature phase diagram of this system and show that unlike the balanced Fermi superfluid there are now two different pseudogap regimes as PG-I and PG-II. While within the PG-I regime both the fermionic species are pseudogapped, PG-II corresponds to the regime where pseudogap feature survives only in the light species. We believe that the single particle spectral features that we discuss in this paper are observable through the species resolved radio frequency spectroscopy and momentum resolved photo emission spectroscopy measurements on systems such as, 6$_{Li}$-40$_{K}$ mixture. We further investigate the interplay between the population and mass imbalances and report that at a fixed population imbalance the BCS-BEC crossover in a Fermi-Fermi mixture would require a critical interaction (U$_{c}$), for the realization of the homogeneous superfluid state. The effect of imbalance in mass on the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase has been probed in detail in terms of the thermodynamic and fermionic behavior of this phase. It has been observed that in spite of the s-wave symmetry of the pairing field a nodal superfluid gap is realized in the LO regime. Our results on the various thermal scales and regimes are expected to serve as benchmarks for the experimental observations on 6$_{Li}$-40$_{K}$ mixture.