Formation of Gapless Phases of $K^0$ Condensed Color-Flavor Locked   Superconducting Quark Matter
  Electric and color neutral solutions, and the critical conditions for the formation of gapless color superconductors, are investigated in $K^0$ condensed color-flavor locked quark matter for nonzero strange quark mass. We show that as the strange quark mass increases, gapless modes for up-strange quark pairing occur first, followed by down-strange quark pairing. The behavior of the gaps, the dispersion relations, and the thermodynamic potential are all found as functions of the strange quark mass on the basis of a Nambu Jona-Lasinio type model. To a high degree of accuracy, they are presented as relatively simple elementary functions. This allows for easy computation for any reasonable range of baryon chemical potential and strange quark mass. 
Xiao-Bing Zhang, J. I. Kapusta