On Anyon Superconductivity

We investigate the statistical mechanics of a gas of fractional statistics particles in 2+1 dimensions. In the case of statistics very close to Fermi statistics (statistical parameter θ=π(1−1/n), for large n), the effect of the statistics is a weak attraction. Building upon earlier RPA calculation of Fetter, Hanna, and Laughlin for the case n=2, we argue that for large n perturbation theory is reliable and exhibits superfluidity (or superconductivity after coupling to electromagnetism). We attempt to describe the order parameter for this superconducting phase in terms of “spontaneous breaking of commutativity of translations” as opposed to the usual pairing order parameters. The vortices of the superconducting anyon gas are charged, and superconducting order parameters of the usual type vanish. We investigate the characteristic P and T violating phenomenology.