Emergence of the geometric contribution to the superfluid density in the inner crust of neutron stars

Abstract

The geometric contribution to the superfluid density has been found to be of great importance in the inner crust of neutron stars. In this work we clarify how this contribution arises in the context of a band theory for neutrons. Specifically, we derive the dependence of the superfluid density on the magnitude of the pairing gap when the system has many bands cutting the Fermi energy, as it is the case for the neutrons in the inner crust. Also, in the perturbation theory framework, we find that it is essential to account for the corrections to the (Bogoliubov) quasi-particle states in order to get the geometric contribution. Accounting only for the corrections to the (Hartree-Fock) single-particle states leads to the conventional contribution only.

Figures (2)

• Figure 1: Single-particle band structure in the simple cubic lattice for a case example in the crystal phase of the inner crust of neutron stars (see Almirante25A for details). $\xi_\alpha=\epsilon_\alpha-\mu$ are HF eigenvalues, the first $70$ bands around the Fermi energy are plotted. The horizontal axis is the Bloch momentum along the high symmetrical path of the simple cubic Brillouin zone Setyawan10.
• Figure 2: Conventional (crosses) and geometric (points) contributions to the superfluid fraction as functions of the pairing gap, computed respectively with Eqs. (\ref{['eq:supdens_conv']}) and (\ref{['eq:supdens_geom']}) for two different baryon densities in the crystal phase of the inner crust of neutron stars (see Almirante25 for details). Lines are linear fits performed in the range $\Delta\in[0.001,0.015]$ MeV.