Topological p{sub x}+ip{sub y} superfluid phase of fermionic polar molecules

We discuss the topological p{sub x}+ip{sub y} superfluid phase in a two-dimensional (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{sub 0}(r) that has an attractive dipole-dipole 1/r{sup 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{sub 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{sub c} can be varied within a few orders of magnitude by modifying the short-range part of the potential V{sub 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 ordermore » of seconds even at 2D densities {approx}10{sup 9} cm{sup -2}. This leads to T{sub c} of up to a few tens of nanokelvins and makes it realistic to obtain the topological p{sub x}+ip{sub y} phase in experiments with ultracold polar molecules.« less