Superfluidity, Sound Velocity and Quasi Condensation in the 2D BCS-BEC Crossover

We study finite-temperature properties of a two-dimensional superfluid made of ultracold alkali-metal atoms in the BCS-BEC crossover. We investigate the region below the critical temperature $T_{BKT}$ of the Berezinskii-Kosterlitz-Thouless phase transition, where there is quasi-condensation, by analyzing the effects of phase and amplitude fluctuations of the order parameter. In particular, we calculate the superfluid fraction, the sound velocity and the quasi-condensate fraction as a function of the temperature and of the binding energy of fermionic pairs.