  In this paper, we put forward to another route realizing topological
superfluid (TS). In contrast to conventional method, spin-orbit coupling and
external magnetic field are not requisite. Introducing an experimentally
feasible technique called on-site rotation (OSR) into p-band honeycomb optical
lattices for spinless Fermi gases and considering CDW and pairing on the same
footing, we investigate the effects of OSR on superfluidity. The results
suggest that when OSR is beyond a critical value, where CDW vanishes, the
system transits from a normal superfluid (NS) with zero TKNN number to TS
labeled by a non-zero TKNN number. In addition, phase transitions between
different TS are also possible.
