Near the flavor SU(3) limit, we propose an analytical description for color-flavorlocked-type Bardeen-Cooper-Schrieffer (BCS) phase in the Nambu Jona-Lasinio (NJL) model. The diquark behaviors in light-flavor and strange-flavor-involved channels and Bose-Einstein condensation (BEC) of bound diquark states are studied. When the attractive interaction between quarks is strong enough, a BCS-BEC crossover is predicted in the environment with color-flavor-locked pairing pattern. The resulting Bose-Einstein condensed phase is found to be an intergrade phase before the emergence of the previous-predicted BEC phase in two-flavor quark superconductor.
In the color-flavor locked quark superconducting phase with the additional chiral condensates, the magnetic effects are investigated within the three-flavor Nambu-Jona-Lasinio framework. Based on the rotated electromagnetic mechanism, we incorporate the effective quark masses into the coexistence phase self-consistently. The numerical calculation shows that the magnetic catalysis of effective masses is different from the known phenomenon that occurs in the unpaired quark matter. Moreover, the interplay between magnetic catalysis and gap splitting is studied for the first time.
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