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We analyze pairing of fermions in two dimensions for fully-gapped cases withbroken parity (P) and time-reversal (T), especially cases in which the gapfunction is an orbital angular momentum ($l$) eigenstate, in particular $l=-1$(p-wave, spinless or spin-triplet) and $l=-2$ (d-wave, spin-singlet). For$l\neq0$, these fall into two phases, weak and strong pairing, which may bedistinguished topologically. In the cases with conserved spin, we deriveexplicitly the Hall conductivity for spin as the corresponding topologicalinvariant. For the spinless p-wave case, the weak-pairing phase has a pairwavefunction that is asympototically the same as that in the Moore-Read(Pfaffian) quantum Hall state, and we argue that its other properties (edgestates, quasihole and toroidal ground states) are also the same, indicatingthat nonabelian statistics is a {\em generic} property of such a paired phase.The strong-pairing phase is an abelian state, and the transition between thetwo phases involves a bulk Majorana fermion, the mass of which changes sign atthe transition. For the d-wave case, we argue that the Haldane-Rezayi state isnot the generic behavior of a phase but describes the asymptotics at thecritical point between weak and strong pairing, and has gapless fermionexcitations in the bulk. In this case the weak-pairing phase is an abelianphase which has been considered previously. In the p-wave case with an unbrokenU(1) symmetry, which can be applied to the double layer quantum Hall problem,the weak-pairing phase has the properties of the 331 state, and with nonzerotunneling there is a transition to the Moore-Read phase. The effects ofdisorder on noninteracting quasiparticles are considered.Comment: Accepted by PRB; references added and typos correcte

Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect