We investigate the superfluid phase transition in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas with mass imbalance. In the presence of mass imbalance, it is known that the strong-coupling Gaussian fluctuation theory, as well as the ordinary non-self-consistent T-matrix theory, that have been extensively used to clarify various BCS-BEC crossover physics in the mass-balanced case, unphysically give double valued superfluid phase transition temperature T c in the crossover region. In our previous paper (R. Hanai et al., J. Low Temp. Phys. 171:389, 2013), this difficulty was shown to be eliminated by an extended T-matrix approximation (ETMA). However, it was also found that this improved theory still gives vanishing T c in the BCS regime, when the mass imbalance ratio remarkably deviates from unity. In this paper, further extending ETMA to include higher order pairing fluctuations to the fully self-consistent T-matrix level, we clarify whether the vanishing T c obtained in ETMA is an intrinsic phenomenon or an artifact of this approximation. We show that the self-consistent T-matrix theory always gives a finite T c, even in the region where ETMA predicts the absence of superfluid instability. The key to the recovery of T c is found to be a consistent treatment with respect to the Fermi surface sizes of the light mass and heavy mass components, which ETMA lacks in. Since Fermi condensates with mass imbalance have been recently discussed in various systems, such as a 40K-6Li Fermi gas, exciton-polariton condensate, as well as color superconductivity, our results would be useful in constructing a reliable strong-coupling theory to examine physical properties of these novel Fermi superfluids.
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