Superconducting order parameter for the even-denominator fractional quantum Hall effect

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.