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Bulletin of the American Physical Society

Correlation-hole induced scillatory pfaffian states in even-denominator fractional quantum Hall effects

Yuan-Ming Lu, Yue Yu, Ziqiang Wang

Published Mar 15, 2010• 0 citations
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The evidence for superconductivity in the even-denominator fractional quantum Hall effect has been so far almost entirely based on a single trial wave function called the Moore-Read Pfaffian wave function with its interpretation as a BCS wave function of composite fermions. While being a dominant candidate, however, the Moore-Read Pfaffian wave function has a number of lingering issues for being an actual ground state of realistic Hamiltonians, which include broken particle-hole symmetry and less than ideal overlap with exact ground states. In this work, we provide direct evidence for superconductivity via exact diagonalization first by demonstrating the even-odd effect in the ground-state energy and then by explicitly computing the superconducting order parameter as a function of the separation distance between two constituent composite fermions in a Cooper pair.
We report on the study of the fractional quantum Hall effect at the filling factor 5/2 using exact diagonalization method with torus geometry. The particle-hole symmetry breaking effect is considered using an additional three-body interaction. Both Pfaffian and anti-Pfaffian states can be the ground state depending on the sign of the three-body interaction. The results of the low-energy spectrum, the wave function overlap, and the particle-hole parity evolution, have shown clear evidence of a direct sharp transition (possibly first order) from the Pfaffian to the anti-Pfaffian state at the Coulomb point. A quantum phase diagram is established, where one finds further transitions from the Pfaffian or anti-Pfaffian state to the nearby compressible phases induced by a change of the pseudopotential.