Superconducting phases in a two-component microscale model of neutron star cores.

We study the ground-state characteristics of two coupled, coexisting superfluid condensates (one neutral, the other electrically charged) by means of a Galilean-invariant, zero-temperature Ginzburg-Landau model. While this framework is applicable to any interacting condensed-matter mixture of a charged and a neutral component, we focus on nuclear matter in neutron star cores, where proton and neutron condensates are coupled via non-dissipative entrainment. By connecting our Ginzburg-Landau energy functional to the Skyrme interaction, we provide a realistic microscale description of the neutron star interior and hence deduce the ground state of the superconducting protons in the presence of a magnetic field. Using the nuclear density as the control parameter, we construct superconducting phase diagrams for six representative Skyrme models, revealing the microphysical magnetic flux distribution throughout the neutron star core. The phase diagrams are rather complex and the locations of most of the phase transitions can only be determined through numerical calculations. Nonetheless, we find that for all equations of state considered in this work, much of the outer core exhibits type-1.5 superconductivity, rather than type-II superconductivity as is generally assumed. For local magnetic field strengths $\lesssim 10^{14} \, \text{G}$, the magnetic flux is distributed inhomogeneously, with bundles of magnetic fluxtubes separated by flux-free Meissner regions. We provide a new criterion to determine the transition between this type-1.5 phase and the type-I region in the inner core.