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

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 $\mu$.

15 pages, 14 figures; accepted for publication in PRD

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• Magnetic catalysis effect in (2+1)-dimensional Gross--Neveu model with Zeeman interaction
• Superconductivity phenomenon induced by external in-plane magnetic field in (2+1)-dimensional Gross--Neveu type model
• Phase diagram of the 2+1-dimensional Gross-Neveu model with chiral imbalance
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• Suppression of superconductivity by inhomogeneous chiral condensation in the NJL${}_2$ model
• Gross-Neveu model with O(2)${}_L\times$O(2)${}_R$ chiral symmetry: Duality with Zakharov-Mikhailov model and large $N$ solution
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