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In this contribution, current status and future prospects of our ongoingproject is summarized. In the inner crust of neutron stars, a variety ofcrystalline structures may emerge, as a result of competition of Coulomb andnuclear interactions, which are immersed in a sea of superfluid neutrons. Thebest quantum mechanical approach to study properties of dripped neutrons undera periodic potential is the band theory of solids. Concerning the bandstructure effects on transport properties of neutrons, however, situation iscomplicated and there has not been established a clear consensus yet. Toprovide a robust conclusion on the band structure effects, we have developed afully-microscopic time-dependent band theory based on time-dependent densityfunctional theory (TDDFT), taking full account of Fermionic superfluditiy. Wehave successfully developed a parallel computational code and applied it to theslab phase of nuclear matter. We introduce ongoing works and discuss possiblefuture directions.

Time-Dependent Superfluid Band Theory for the Inner Crust of Neutron Stars: Current Status and Future Challenges