Anyon superconductivity at rational statistics

Abstract

We study the anyon gas with repulsive interactions at θ = π(1-1/ν), where ν is a fractional-quantum-Hall-effect filling fraction, using Jain’s composite-fermion and decomposition-of-fermion techniques. In the first case, the anyon gas forms a superconducting state, which, however, is the same as the state that occurs at ν = m, where m is an integer, with no repulsive interactions. In the second approach, the anyon gas forms correlated states that are superconducting at ν⁻¹ = Σ^p_I = 1/m_I, with p an odd integer and m_I an integer.