Abstract
It is expected that in the interior of compact stars a proton superconductor coexists with and couples to a neutron superfluid. Starting from a field-theoretical model for two complex scalar fields - one of which is electrically charged - we derive a Ginzburg-Landau potential which includes entrainment between the two fluids and temperature effects from thermal excitations of the two scalar fields and the gauge field. The Ginzburg-Landau description is then used for an analysis of the phase structure in the presence of an external magnetic field. In particular, we study the effect of the superfluid on the flux tube phase by computing the various critical magnetic fields and deriving an approximation for the flux tube interaction. As a result, we point out differences to the naive expectations from an isolated superconductor, for instance the existence of a first-order flux tube onset, resulting in a more complicated phase structure in the region between type-I and type-II superconductivity.
Highlights
Introduction and main resultsIn the dense environment of compact stars, nucleons can form Cooper pairs, just like electrons in an ordinary superconductor [1, 2]
Temperature effects become important because the critical temperature is of the same order of magnitude as the pairing gap and can become very small too
The same is true for the critical magnetic fields: if the pairing gap is small, only a small magnetic field is needed to either penetrate into the superconductor through flux tubes or to break superconductivity completely
Summary
In the dense environment of compact stars, nucleons can form Cooper pairs, just like electrons in an ordinary superconductor [1, 2]. If we start from a phase where superfluid and superconductor coexist, increasing the temperature may lead us to a pure superfluid phase or a pure superconducting phase, depending on the values of the self- and cross-couplings We could consider topological defects of the neutral condensate instead of the charged condensate This scenario, superfluid vortices getting magnetized through entrainment of a charged fluid, is relevant for dense nuclear matter inside a compact star [9, 10], and it would be interesting to see whether our numerical calculation of the vortex profile, taking into account the coupling between the fluids from a "microscopic" point of view, agrees with or possibly goes beyond the traditional approaches in the literature. Both fields can be charged: two-component superconductors can be realized for instance in two-band superconductors [15], in liquid metallic hydrogen [16], or possibly in compact stars if charged hyperons form Cooper pairs [17]
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