Superfluidity, sound velocity, and quasicondensation in the two-dimensional 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 TBKT of the Berezinskii-Kosterlitz-Thouless phase transition where there is quasicondensation 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 quasicondensate fraction as a function of the temperature and of the binding energy of fermionic pairs.