Superfluid fraction in the rod phase of the inner crust of neutron stars

The rod phase as it is expected in the bottom layers of neutron-star crusts is analyzed within the Hartree-Fock-Bogoliubov framework. To well describe the interplay between band structure and superfluidity, periodicity of the lattice is taken into account using Bloch boundary conditions. A relative flow between the rods and the surrounding neutron gas is introduced in a time-independent way. This induces a nontrivial phase of the complex order parameter, leading to a counterflow between neutrons inside and outside the rods. With the resulting current, we compute the actual neutron superfluid fraction. For the latter our results are significantly larger than previous ones obtained in normal band theory, indicating that the normal band theory overestimates the entrainment effect.