Color superconductivity and gapless modes in strange quark matter at finite temperatures

We investigate the phase diagram of strange quark matter in beta equilibrium where the lighter up and down quarks form the two flavor superconducting matter whereas the strange quark remains unpaired. This is studied within a Nambu-Jona-Lasinio model. The variational method as used here allows us to investigate simultaneous formation of condensates in quark-antiquark as well as in diquark channels. Color and electric charge neutrality conditions are imposed in the calculation of the thermodynamic potential. Medium dependence of strange quark mass plays a sensitive role in maintaining charge neutrality conditions. At zero temperature the system goes from the gapless phase to the usual BCS phase through an intermediate normal phase as density is increased. However, at higher temperature the gapless to BCS transition becomes a smooth transition. The gapless modes show a smooth behavior with respect to temperature vanishing above a critical temperature which is larger than the BCS transition temperature