Title: P-wave superfluidity of atomic lattice fermions,
Abstract: We discuss the emergence of p-wave superfluidity of identical atomic fermions
in a two-dimensional optical lattice. The optical lattice potential manifests
itself in an interplay between an increase in the density of states on the
Fermi surface and the modification of the fermion-fermion interaction
(scattering) amplitude. The density of states is enhanced due to an increase of
the effective mass of atoms. In deep lattices the scattering amplitude is
strongly reduced compared to free space due to a small overlap of wavefunctions
of fermion sitting in the neighboring lattice sites, which suppresses the
p-wave superfluidity. However, for moderate lattice depths the enhancement of
the density of states can compensate the decrease of the scattering amplitude.
Moreover, the lattice setup significantly reduces inelastic collisional losses,
which allows one to get closer to a p-wave Feshbach resonance. This opens
possibilities to obtain the topological $p_x+ip_y$ superfluid phase, especially
in the recently proposed subwavelength lattices. We demonstrate this for the
two-dimensional version of the Kronig-Penney model allowing a transparent
physical analysis.