The Minimal CFL-Nuclear Interface

At nuclear matter density, electrically neutral strongly interacting matter in weak equilibrium is made of neutrons, protons and electrons. At sufficiently high density, such matter is made of up, down and strange quarks in the colorflavor locked phase, with no electrons. As a function of increasing density (or, perhaps, increasing depth in a compact star) other phases may intervene between these two phases which are guaranteed to be present. The simplest possibility, however, is a single first order phase transition between CFL and nuclear matter. Such a transition, in space, could take place either through a mixed phase region or at a single sharp interface with electron-free CFL and electron-rich nuclear matter in stable contact. Here we construct a model for such an interface. It is characterized by a region of separated charge, similar to an inversion layer at a metal-insulator boundary. On the CFL side, the charged boundary layer is dominated by a condensate of negative kaons. We then consider the energetics of the mixed phase alternative. We find that the mixed phase will occur only if the nuclear-CFL surface tension is significantly smaller than dimensional analysis would indicate.