  We investigate the vacuum structure of dense quark matter in strong magnetic
fields at finite temperature and densities in a 3 flavor Nambu Jona Lasinio
(NJL) model including the Kobayashi-Maskawa-t'Hooft (KMT) determinant term
using a variational method. The method uses an explicit structure for the
`ground' state in terms of quark-antiquark condensates as well as diquark
condensates. The mass gap equations and the superconducting gap equations are
solved self consistently and are used to compute the thermodynamic potential
along with the charge neutrality conditions. We also derive the equation of
state for the charge neutral strange quark matter in the presence of strong
magnetic fields which could be relevant for neutron stars.
