  We address the phase structure of color superconducting quark matter at high
quark density. Under the electric and color neutrality conditions there appear
various phases as a result of the Fermi surface mismatch among different quark
flavors induced by finite strange quark mass; the color-flavor locked (CFL)
phase where quarks are all energy gapped, the u-quark superconducting (uSC)
phase where u-quarks are paired with either d- or s-quarks, the d-quark
superconducting (dSC) phase that is the d-quark analogue of the uSC phase, the
two-flavor superconducting (2SC) phase where u- and d-quarks are paired, and
the unpaired quark matter (UQM) that is normal quark matter without pairing.
Besides these possibilities, when the Fermi surface mismatch is large enough to
surpass the gap energy, the gapless superconducting phases are expected. We
focus our discussion on the chromomagnetic instability problem related to the
gapless CFL (gCFL) onset and explore the instability regions on the phase
diagram as a function of the temperature and the quark chemical potential. We
sketch how to reach stable physical states inside the instability regions.
