Superconducting phase transitions induced by chemical potential in (2+1)-dimensional four-fermion quantum field theory

TL;DR

This paper investigates how chemical potential influences phase transitions in a (2+1)-dimensional four-fermion quantum field theory, revealing conditions for superconducting phases at various temperatures and interaction strengths.

Contribution

It extends a (1+1)-dimensional model to (2+1) dimensions, analyzing phase transitions with both chiral and superconducting interactions using large-N expansion.

Findings

Superconducting phase appears at large chemical potential and any coupling.

Cooper pairing occurs at zero temperature for weak chiral interactions.

Superconducting phase exists at finite temperature under certain conditions.

Abstract

In the paper a generalization of the (1+1)-dimensional model by Chodos et al [Phys. Rev. D61, 045011 (2000)] has been performed to the case of (2+1)-dimensional spacetime. The model includes four-fermion interaction both in the fermion-antifermion (or chiral) and fermion-fermion (or superconducting) channels. We study temperature $T$ and chemical potential $\mu$ induced phase transitions in the leading order of large-$N$ expansion technique, where $N$ is a number of fermion fields. It is shown that at sufficiently large values of $\mu$ and arbitrary relations between coupling constants, superconducting phase appears in the system both at T=0 and $T>0$. In particular, at T=0 and sufficiently weak attractive interaction in the chiral channel, the Cooper pairing occurs for arbitrary couplings in the superconducting channel even at infinitesimal values of $\mu$.