Quantum phase transitions and the ν=5/2 fractional hall state in wide quantum wells

We study the nature of the ν=5/2 quantum Hall state in wide quantum wells under the mixing of electronic subbands and Landau levels. A general method is introduced to analyze the Moore-Read Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, under periodic boundary conditions in a "quartered" Brillouin zone scheme containing both even and odd numbers of electrons. By examining the rotational quantum numbers on the torus, we show spontaneous breaking of the particle-hole symmetry can be observed in finite-size systems. In the presence of electronic-subband and Landau-level mixing, the particle-hole symmetry is broken in such a way that the anti-Pfaffian state is unambiguously favored, and becomes more robust in the vicinity of a transition to the compressible phase, in agreement with recent experiments.