Pfaffian paired states at filling factor 5/2

Within the Dirac composite fermion theory of fractional quantum Hall effect (FQHE), we investigate which Pfaffian paired state will dominate at a fixed value of a particle-hole (PH) symmetry breaking parameter - the mass of Dirac composite fermions. The Dirac mass mimics the presence of Landau level mixing in experiments. We demonstrate that the presence of mass stabilizes PH Pfaffian topological pairing contrary to our naive expectation that the PH Pfaffian will be relevant for the (zero-mass) PH symmetric case. Using only field theoretical means we show that, due to gauge field effects, there is a strong competition among Pfaffians; depending on the sign of mass, Pfaffian or anti-Pfaffian will dominate for small masses, consistent with numerical experiments at filling factor 5/2, and PH Pfaffian may be present for larger masses. L. Antonic, J. Vucicevic, and M.V. Milovanovic, Paired states at 5/2 : Particle-hole Pfaffian and particle-hole symmetry breaking, Physical Review B 98, 115107 (2018).