Topological superfluid state of fermions on a p-band optical square lattice

In this paper we study an interacting mixture of ultracold spinless fermions on the $s$ band and bosons on the $p$ band in a 2D square optical lattice, of which the effective model is reduced to a $p$-band fermionic system with nearest-neighbor attractive interaction. From this effective $p$-band model, we find a translation symmetry protected ${\mathbb{Z}}_{2}$ topological superfluid that is characterized by a special fermion parity pattern at high-symmetry points in momentum space $\mathbf{k}=(0,0)$, $(0,\ensuremath{\pi})$, $(\ensuremath{\pi},0)$, $(\ensuremath{\pi},\ensuremath{\pi})$. Such ${\mathbb{Z}}_{2}$ topological superfluid supports the robust Majorana edge modes and a new type of low-energy excitation---(supersymmetric) ${\mathbb{Z}}_{2}$ link excitation.