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The electric/color neutral solution and the critical conditions for gapless formation are investigated in the $K^0$ condensed color-flavor locked matter. We point out that there exist no longer gapless modes for down-strange quark pairing while the gapless phenomenon for up-strange one is dominated in the $K^0$ condensed environment. In a model-independent way, the phase transition to the resulting gapless phase is found to be of first-order. The novel phase structure implies that the chromomagnetic instability happens in the previous-predicted gapless phase might be removed at least partly

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Formation of gapless phases of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>K</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math>condensed color-flavor locked superconducting quark matter

Formation of gapless phases ofK0condensed color-flavor locked superconducting quark matter