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We investigate the superfluid phase transition and effects of mass imbalance in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an cold Fermi gas. We point out that the Gaussian fluctuation theory developed by Nozières and Schmitt-Rink and the T-matrix theory, that are now widely used to study strong-coupling physics of cold Fermi gases, give unphysical results in the presence of mass imbalance. To overcome this problem, we extend the T-matrix theory to include higher-order pairing fluctuations. Using this, we examine how the mass imbalance affects the superfluid phase transition. Since the mass imbalance is an important key in various Fermi superfluids, such as K-Li Fermi gas mixture, exciton condensate, and color superconductivity in a dense quark matter, our results would be useful for the study of these recently developing superfluid systems. [ABSTRACT FROM AUTHOR]

We study cold fermions in 2D that are interacting through the s-wave contact potential, using the path-integral formalism. The phase transitions are investigated using the joint solution of the gap and number equations. In the latter ones, the amplitude and phase fluctuations are taken into account within the t-matrix NSR-type formalism. It is shown that convergent solutions for the fermion density in 2D can be obtained even in the lowest-order (quadratic) approximation for fluctuations with a proper determination of the spectral functions. This approach leads, in particular, to a non-coherent quasicondensate which exists between the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature below which the system is superfluid and a transition temperature T above which the quasicondensate is destroyed. [ABSTRACT FROM AUTHOR]