Paired states of fermions in two dimensions with breaking of parity and timereversal symmetries and the fractional quantum Hall effect
Abstract
We analyze pairing of fermions in two dimensions for fully gapped cases with broken parity (P) and time reversal (T), especially cases in which the gap function 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≠0, these fall into two phases, weak and strong pairing, which may be distinguished topologically. In the cases with conserved spin, we derive explicitly the Hall conductivity for spin as the corresponding topological invariant. For the spinless pwave case, the weakpairing phase has a pair wave function that is asympototically the same as that in the MooreRead (Pfaffian) quantum Hall state, and we argue that its other properties (edge states, quasihole, and toroidal ground states) are also the same, indicating that nonabelian statistics is a generic property of such a paired phase. The strongpairing phase is an abelian state, and the transition between the two phases involves a bulk Majorana fermion, the mass of which changes sign at the transition. For the dwave case, we argue that the HaldaneRezayi state is not the generic behavior of a phase but describes the asymptotics at the critical point between weak and strong pairing, and has gapless fermion excitations in the bulk. In this case the weakpairing phase is an abelian phase, which has been considered previously. In the pwave case with an unbroken U(1) symmetry, which can be applied to the double layer quantum Hall problem, the weakpairing phase has the properties of the 331 state, and with nonzero tunneling there is a transition to the MooreRead phase. The effects of disorder on noninteracting quasiparticles are considered. The gapped phases survive, but there is an intermediate thermally conducting phase in the spinless pwave case, in which the quasiparticles are extended.
 Publication:

Physical Review B
 Pub Date:
 April 2000
 DOI:
 10.1103/PhysRevB.61.10267
 arXiv:
 arXiv:condmat/9906453
 Bibcode:
 2000PhRvB..6110267R
 Keywords:

 73.40.Hm;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Superconductivity;
 High Energy Physics  Theory
 EPrint:
 Accepted by PRB