Title: Critical magnetic fields in a superconductor coupled to a superfluid,
Abstract: We study a superconductor that is coupled to a superfluid via density and
derivative couplings. Starting from a Lagrangian for two complex scalar fields,
we derive a temperature-dependent Ginzburg-Landau potential, which is then used
to compute the phase diagram at nonzero temperature and external magnetic
field. This includes the calculation of the critical magnetic fields for the
transition to an array of magnetic flux tubes, based on an approximation for
the interaction between the flux tubes. We find that the transition region
between type-I and type-II superconductivity changes qualitatively due to the
presence of the superfluid: the phase transitions at the upper and lower
critical fields in the type-II regime become first order, opening the
possibility of clustered flux tube phases. These flux tube clusters may be
realized in the core of neutron stars, where superconducting protons are
expected to be coupled to superfluid neutrons.