  The interplay between dimensionality, coherence and interaction in superfluid
Fermi gases is analyzed by the phase correlation function of the field of
fermionic pairs. We calculate this phase correlation function for a
two-dimensional superfluid Fermi gas with $s$-wave interactions within the
Gaussian pair fluctuation formalism. The spatial behavior of the correlation
function is shown to exhibit a rapid (exponential) decay at short distances and
a characteristic algebraic decay at large distances, with an exponent matching
that expected from Berezinskii-Kosterlitz-Thouless theory of 2D Bose
superfluids. We conclude that the Gaussian pair fluctuation approximation is
able to capture the physics of quasi long-range order in two-dimensional Fermi
gases.
