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
GD​/GS​, where the 2SC phase is preferred, we see hints of the
Clogston-Chandrasekhar limit at a very large value of the magnetic field
(B∼1019G), but this limit is strongly affected by Shubnikov de
Haas-van Alphen oscillations of the gap, indicating the transition to a
domain-like state.Comment: 19 pages, 7 figures, Matches with the published versio