Chiral symmetry breaking, color superconductivity, and equation of state for magnetized strange quark matter

We investigate the vacuum structure of dense quark matter in strong magnetic fields in a three-flavor Nambu Jona Lasinio (NJL) model including the Kobayashi-Maskawa-t'Hooft (KMT) determinant term using a variational method. The method uses an explicit construct for the "ground" state in terms of quark-antiquark condensates as well as diquark condensates in the background of a constant magnetic field. The coupled mass gap equations and the superconducting gap equation are solved self-consistently and are used to compute the thermodynamic potential along with charge neutrality conditions imposed for bulk matter. Within the model, we observe inverse magnetic catalysis for chiral symmetry breaking for moderate magnetic fields. Further, we observe gapless modes in the presence of the magnetic field when charge neutrality conditions are imposed. The equation of state for charge neutral magnetized strange quark matter is derived, and found to be stiffer compared to the vanishing magnetic field counterpart. This could be relevant for gross structural properties of neutron stars.