Topological p_x+ip_y Superfluid Phase of Fermionic Polar Molecules

We discuss the topological p_x+ip_y superfluid phase in a 2D gas of single-component fermionic polar molecules dressed by a circularly polarized microwave field. This phase emerges because the molecules may interact with each other via a potential V_0(r) that has an attractive dipole-dipole 1/r^3 tail, which provides p-wave superfluid pairing at fairly high temperatures. We calculate the amplitude of elastic p-wave scattering in the potential V_0(r) taking into account both the anomalous scattering due to the dipole-dipole tail and the short-range contribution. This amplitude is then used for the analytical and numerical solution of the renormalized BCS gap equation which includes the second order Gor'kov-Melik-Barkhudarov corrections and the correction related to the effective mass of the quasiparticles. We find that the critical temperature T_c can be varied within a few orders of magnitude by modifying the short-range part of the potential V_0(r). The decay of the system via collisional relaxation of molecules to dressed states with lower energies is rather slow due to the necessity of a large momentum transfer. The presence of a constant transverse electric field reduces the inelastic rate, and the lifetime of the system can be of the order of seconds even at 2D densities ~ 10^9 cm^{-2}. This leads to T_c of up to a few tens of nanokelvins and makes it realistic to obtain the topological p_x+ip_y phase in experiments with ultracold polar molecules.