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. 
K. Iida, T. Matsuura, M. Tachibana, and T. Hatsuda