The Topological Phase Transition Of Asymmetric Two-component Fermi Gas In Two Dimensions

Recently, asymmetric two-component ultracold Fermi gas has attracted more and more interest. The classical BCS theory of superconductivity describes pairing between opposite-spin fermions near a single Fermi surface. When the fermions of two species has different densities,effective masses, or chemical potentials, Sarma superfluidity may occur, which has unmatched Fermi surfaces. However two-dimensional (2D) Fermi gases have also striking features not encountered in three dimension. Two-body attraction is introduced in 2D. In this thesis we introduce functional integral formalism to derive the self-consistence equations. We investigate superfluid phase and phase transition in 2D at zero temperature for asymmetric Fermi gas. We identify regions corresponding to normal, Sarma phase for different polarization, or mass ratio and discuss topological phase transition in the BCS-BEC crossover. We find topological phase diagram in this region. Then we consider extended BCS theory and off-diagonal long-range order of system as a reliable approximation for studying BCS-BEC crossover at zero temperature. Here we plot condensate fraction of Fermi pairs as function with population imbalance and bound state energy by using numerical calculation.