Neutrality of a magnetized two-flavor quark superconductor

TL;DR

This paper explores how electric and color charge neutrality influence the behavior of magnetized two-flavor quark matter, revealing phase transitions and oscillations in the presence of strong magnetic fields using the NJL model.

Contribution

It provides new insights into the effects of charge neutrality on the 2SC phase under magnetic fields, including the transition to a domain-like state and oscillatory phenomena.

Findings

Magnetic fields induce a crossover in the g2SC phase.

Chiral phase transition remains first order under strong magnetic fields.

Hints of the Clogston-Chandrasekhar limit at extremely high magnetic fields.

Abstract

We investigate the effect of electric and color charge neutrality on the two-flavor color superconducting (2SC) phase of cold and dense quark matter in presence of constant external magnetic fields and at moderate baryon densities. Within the framework of the Nambu-Jona-Lasinio (NJL) model, we study the inter-dependent evolution of the quark's BCS gap and constituent mass with increasing density and magnetic field. While confirming previous results derived for the highly magnetized 2SC phase with color neutrality alone, we obtain new results as a consequence of imposing charge neutrality. In the charge neutral gapless 2SC phase (g2SC), a large magnetic field drives the color superconducting phase transition to a crossover, while the chiral phase transition is first order. At larger diquark-to-scalar coupling ratio $G_D/G_S$, where the 2SC phase is preferred, we see hints of the Clogston-Chandrasekhar limit at a very large value of the magnetic field ($B\sim 10^{19}$G), but this limit is strongly affected by Shubnikov de Haas-van Alphen oscillations of the gap, indicating the transition to a domain-like state.