We investigate the superfluid phase transition and single-particle excitations in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an unpolarized ultracold Fermi gas with mass imbalance (where two different species contributing to Cooper pairs have different atomic masses). In our recent paper [R. Hanai et al., Phys. Rev. A 88, 053621 (2013)], we showed that an extended $T$-matrix approximation (ETMA) can overcome the serious problem known in the ordinary (non-self-consistent) $T$-matrix approximation that it unphysically gives double-valued superfluid phase transition temperature $T_{\mathrm{c}}$ in the presence of mass imbalance. However, at the same time, the ETMA was also found to give the vanishing $T_{\mathrm{c}}$ in the weak-coupling and highly mass-imbalanced case. In this paper, we inspect the correctness of this ETMA result, using the self-consistent $T$-matrix approximation (SCTMA). We show that the vanishing $T_{\mathrm{c}}$ is an artifact of the ETMA, coming from an internal inconsistency of this theory. The superfluid phase transition actually always occurs, irrespective of the ratio of mass imbalance. We also apply the SCTMA to the pseudogap problem in a mass-imbalanced Fermi gas. We show that pairing fluctuations induce different pseudogap phenomena between the light component and heavy component. We also point out that a ${}^6\mathrm{Li}-{}^{40}\mathrm{K}$ mixture is a useful system for the realization of a heteropairing state, as well as for the study of component-dependent pseudogap phenomena.

• Received 27 July 2014

DOI:https://doi.org/10.1103/PhysRevA.90.043622