Suppression of superconductivity by inhomogeneous chiral condensation in the NJL$_2$ model

TL;DR

This paper explores how inhomogeneous chiral condensates can suppress superconductivity in a (1+1)-dimensional NJL model, revealing phase interactions at nonzero temperature and chemical potential.

Contribution

It demonstrates that spatially inhomogeneous chiral phases can inhibit superconductivity when certain coupling conditions are met, extending previous homogeneous models.

Findings

Inhomogeneous chiral phases suppress superconductivity for G1>G2.

Superconducting phase exists at high chemical potential in homogeneous models.

Inhomogeneity leads to new phase interactions not seen in earlier models.

Abstract

We investigate the possibility of spatially inhomogeneous chiral and Cooper, or superconducting, pairing in the (1+1)-dimensional model by Chodos et al [ Phys. Rev. D61, 045011 (2000)] generalized to continuous chiral invariance. The consideration is performed at nonzero temperature $T$ and quark number chemical potential $\mu$. It is shown in the framework of the Fulde--Ferrel inhomogeneity ansatz for chiral and Cooper condensates that if $G_1>G_2$, where $G_1$ and $G_2$ are the coupling constants in the quark-antiquark and diquark channels, then in the $(\mu,T)$-phase diagram the superconducting phase is suppressed by spatially inhomogeneous chiral spiral phase with broken chiral symmetry. In contrast, in the above mentioned original Chodos et al model, where only the opportunity for homogeneous condensates were taken into account, the superconducting phase is realized at sufficiently high values of $\mu$ at arbitrary values of $G_2>0$, including the interval $0<G_2<G_1$.