Phase structure of two-flavor quark matter: Heterogeneous superconductors

We analyze the free energy of charge- and color-neutral two-flavor quark matter within the BCS approximation. We consider both the homogeneous gapless superconducting phase and the heterogeneous mixed phase where normal and BCS superconducting phases coexist. We calculate the surface tension between normal and superconducting phases and use it to compare the free energies of the gapless and mixed phases. Our calculation, which retains only the leading-order gradient contribution to the free energy and ignores finite size effects such as Debye screening, indicates that the mixed phase is energetically favored over an interesting range of densities of relevance to two-flavor quark matter in neutron stars.