FIELD-THEORETICAL ANALYSIS OF ANYONIC SUPERCONDUCTIVITY

Abstract

We derive several results pertaining to anyonic superconductivity as described by a Chern-Simons field theory. (1) The renormalized Chern-Simons term at finite density is shown to vanish when the renormalized coefficient at zero density takes values Ne2/2π. This is the field-theoretical requirement to have a massless pole in the current-current correlator. We can then show that in the Chern-Simons description a system of charged anyons at zero temperature is a superconductor. This result is shown to hold to all orders in perturbation theory by generalizing a nonrenormalization theorem of the zero density case. (2) At finite temperature the renormalized Chern-Simons term does not vanish at the one-loop perturbative level. We compute the mass of this apparent “pseudo-Goldstone mode”. We also exhibit an effect suggestive of critical behavior, for this same system, at a nonzero Tc. We discuss the possible implications of these perturbative results. (3) A low energy effective action for an anyonic superconductor is derived directly from Chern-Simons field theory. Several P and T violating effects occur.