Thermal phase transitions and gapless quark spectra in quark matter at high density

Thermal color superconducting phase transitions in three-flavor quark matter at high baryon density are investigated in the Ginzburg-Landau (GL) approach. We constructed the GL potential near the boundary with a normal phase by taking into account nonzero quark masses, electric charge neutrality, and color charge neutrality. We found that the density of states averaged over paired quarks plays a crucial role in determining the phases near the boundary. By performing a weak coupling calculation of the parameters characterizing the GL potential terms of second order in the pairing gap, we show that three successive second-order phase transitions take place as the temperature increases: a modified color-flavor locked phase (ud, ds, and us pairings) → a dSC phase (ud and ds pairings) → an isoscalar pairing phase (ud pairing) → a normal phase (no pairing). The Meissner masses of the gluons and the number of gapless quark modes are also studied analytically in each of these phases.