  Two-dimensional spin-1/2 fermions with the finite-range interaction are
theoretically studied. Characterizing the attractive interaction in terms of
the scattering length and the effective range, we discuss the finite-range
effects on the ground-state properties in this system. The Brueckner $G$-matrix
approach is employed to analyze the finite-range effects on an attractive
Fermi-polaron energy and the equation of state throughout the BEC-BCS crossover
in two dimensions, which can be realized in the population-imbalanced and
-balanced cases between two components, respectively. The analytical formulae
for these ground states obtained in this study would be useful for
understanding many-body phenomena with finite-range interactions in
low-dimensional systems.
