Emergence of the Geometric Contribution to the Superfluid Density in the Inner Crust of Neutron Stars

The geometric contribution to 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 is the case for neutrons in the inner crust. Also, in the perturbation theory framework, we find that it is essential to account for corrections to (Bogoliubov) quasi-particle states in order to obtain the geometric contribution. Accounting only for the corrections to (Hartree–Fock) single-particle states leads to the conventional contribution only.