Isospin asymmetric matter in uniform and nonuniform strong magnetic fields

Isospin asymmetric quark matter is investigated with the Polyakov Nambu-Jona-Lasinio model at zero temperature in a strong magnetic field. The isospin symmetry/asymmetry can be controlled by altering the fraction parameter alpha of the two kinds of interactions, i.e., the scalar coupling and instanton-induced coupling. Specially, the flavor decoupled state with alpha = 0 is strongly isospin asymmetric. It is accompanied by the discrepancy of the u and d quarks in the chiral phase transitions, which is eliminated up to alpha = 0.5. It is found that there exists a critical value alpha c, above which the simultaneous chiral restoration would happen for the flavor isodoublet, no matter whether their masses are equal or not. The alpha c can be decreased by the increase of the magnetic field. Finally, it is suggested that the presence of the Polyakov potential increases the maximum central magnetic field of compact stars up to 3.5 x 10(18) G.