  We theoretically investigate the Bardeen-Cooper-Schrieffer (BCS) to
Bose-Einstein condensation (BEC) crossover in a two-dimensional Fermi gas with
the finite-range interaction by using the Hartree-Fock-Bogoliubov theory.
Expanding the scattering phase shift in terms of the scattering length and
effective range, we discuss the effect of the finite-range interaction on the
pairing and thermodynamic properties. By solving the gap equation and the
number equation self-consistently, we numerically calculate the effective-range
dependence of the pairing gap, chemical potential, and pair size throughout the
BCS-BEC crossover. Our results would be useful for further understanding of
low-dimensional many-body problems.
