Superconductivity in $2+1$ dimensions via Kosterlitz-Thouless Mechanism: Large-N and Finite-Temperature Analyses

TL;DR

This paper investigates a 2+1 dimensional model with charged fermions, revealing a rich phase structure with superconductivity driven by vortex confinement, and analyzes the effects of temperature and large-N expansion on these phases.

Contribution

It provides a large-N, finite-temperature analysis of superconductivity via the Kosterlitz-Thouless mechanism in a relativistic fermion model, highlighting vortex dynamics and phase transitions.

Findings

Superconductivity occurs at low temperatures due to vortex confinement.

A sequence of phases includes confined-vortex, deconfined-vortex, and normal phases.

The energy gap to T_c ratio exceeds the BCS value for N less than about 22.

Abstract

We analyse 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 non-zero temperature, the model nevertheless exhibits a rich phase structure in the strong coupling r\'egime, because of the non-vanishing VEV of a neutral order parameter and due to the non-trivial dynamics of the vortex excitations on the plane. These are: 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 $T_c$ is bigger than the conventional BCS value, for $N\ltwid 22$.