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We identify the possible ground states for a mixture of two superfluidcondensates (one neutral, the other electrically charged) using aphenomenological Ginzburg-Landau model. While this framework is applicable toany interacting condensed-matter mixture of a charged and a neutral component,we focus on nuclear matter in neutron star cores, where proton and neutroncondensates are coupled via non-dissipative entrainment. We employ the Skyrmeinteraction to determine the neutron star's equilibrium composition, and henceobtain realistic coefficients for our Ginzburg-Landau model at each depthwithin the star's core. We then use the Ginzburg-Landau model to determine theground state in the presence of a magnetic field. In this way, we obtainsuperconducting phase diagrams for six representative Skyrme models, revealingthe microphysical magnetic flux distribution throughout the neutron star core.The phase diagrams are rather complex and the locations of most of the phasetransitions can only be determined through numerical calculations. Nonetheless,we find that for all equations of state considered in this work, much of theouter core exhibits type-1.5 superconductivity, rather than type-IIsuperconductivity as is generally assumed. For local magnetic field strengths$\lesssim 10^{14} \, {\rm G}$, the magnetic flux is distributedinhomogeneously, with bundles of magnetic fluxtubes separated by flux-freeMeissner regions. We provide an approximate criterion to determine thetransition between this type-1.5 phase and the type-I region in the inner core.

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