SUPERCONDUCTIVITY IN 2+1 DIMENSIONS VIA KOSTERLITZ-THOULESS MECHANISM: LARGE N AND FINITE TEMPERATURE ANALYSES

We analyze a (2+1)-dimensional model with charged, relativistic fermions interacting through a four-fermi term. Taking advantage of its large N renormalizability, the various phases of this model are studied at finite temperature and beyond the leading order in 1/N. Although the vacuum expectation value (VEV) of a charged order parameter is zero at any nonzero temperature, the model nevertheless exhibits a rich phase structure in the strong coupling regime, because of the nonvanishing VEV of a neutral order parameter and due to the nontrivial dynamics of the vortex excitations on the plane. These include a confined vortex phase which is superconducting at low temperatures, an intermediate temperature phase with deconfined vortices, and a high temperature phase, where the neutral order parameter vanishes. The manifestation of superconductivity at low temperatures and its disappearance above a critical temperature is explicitly shown to be due to the vortex confinement/deconfinement mechanism of Kosterlitz and Thouless. The ground state does not break parity or time reversal symmetries and the ratio of the energy gap to Tc is bigger than the conventional BCS value, for N≲22.