A low energy theory for superfluid and solid matter and its application to the neutron star crust

TL;DR

This paper develops a low energy effective theory for matter that is both solid and superfluid, applying it to the neutron star crust to understand the interplay of lattice and superfluid components.

Contribution

It formulates a comprehensive effective theory for solid-superfluid phases, including entrainment effects, and applies it specifically to neutron star crusts.

Findings

The theory captures the coupling between lattice and superfluid modes.

Entrainment effects are derived from the underlying particle interactions.

Application to neutron star crust explains the coexistence of nuclei lattice and neutron superfluid.

Abstract

We formulate a low energy effective theory describing phases of matter that are both solid and superfluid. These systems simultaneously break translational symmetry and the phase symmetry associated with particle number. The symmetries restrict the combinations of terms that can appear in the effective action and the lowest order terms featuring equal number of derivatives and Goldstone fields are completely specified by the thermodynamic free energy, or equivalently by the long-wavelength limit of static correlation functions in the ground state. We show that the underlying interaction between particles that constitute the lattice and the superfluid gives rise to entrainment, and mixing between the Goldstone modes. As a concrete example we discuss the low energy theory for the inner crust of a neutron star, where a lattice of ionized nuclei coexists with a neutron superfluid.