Flux tubes and the type-I/type-II transition in a superconductor coupled to a superfluid

TL;DR

This paper investigates how density and gradient couplings between a superconductor and superfluid affect flux tube behavior and the type-I/type-II transition, revealing complex phase structures and metastable states.

Contribution

It introduces a Ginzburg-Landau model with density and gradient couplings to analyze flux tubes, uncovering new phenomena like type-II(n) phases and spinodal regions.

Findings

Density coupling raises the critical kappa for the transition.

High neutron density leads to multiple flux quantum phases.

Gradient coupling lowers the critical kappa and induces spinodal regions.

Abstract

We analyze magnetic flux tubes at zero temperature in a superconductor that is coupled to a superfluid via both density and gradient (``entrainment'') interactions. The example we have in mind is high-density nuclear matter, which is a proton superconductor and a neutron superfluid, but our treatment is general and simple, modeling the interactions as a Ginzburg-Landau effective theory with four-fermion couplings, including only s-wave pairing. We numerically solve the field equations for flux tubes with an arbitrary number of flux quanta, and compare their energies. This allows us to map the type-I/type-II transition in the superconductor, which occurs at the conventional kappa = 1/sqrt(2) if the condensates are uncoupled. We find that a density coupling between the condensates raises the critical kappa and, for a sufficiently high neutron density, resolves the type-I/type-II transition line into an infinite number of bands corresponding to ``type-II(n)'' phases, in which n, the number of quanta in the favored flux tube, steps from 1 to infinity. For lower neutron density, the coupling creates spinodal regions around the type-I/type-II boundary, in which metastable flux configurations are possible. We find that a gradient coupling between the condensates lowers the critical kappa and creates spinodal regions. These exotic phenomena may not occur in nuclear matter, which is thought to be deep in the type-II region, but might be observed in condensed matter systems.