  In this contribution, current status and future prospects of our ongoing
project is summarized. In the inner crust of neutron stars, a variety of
crystalline structures may emerge, as a result of competition of Coulomb and
nuclear interactions, which are immersed in a sea of superfluid neutrons. The
best quantum mechanical approach to study properties of dripped neutrons under
a periodic potential is the band theory of solids. Concerning the band
structure effects on transport properties of neutrons, however, situation is
complicated and there has not been established a clear consensus yet. To
provide a robust conclusion on the band structure effects, we have developed a
fully-microscopic time-dependent band theory based on time-dependent density
functional theory (TDDFT), taking full account of Fermionic superfluditiy. We
have successfully developed a parallel computational code and applied it to the
slab phase of nuclear matter. We introduce ongoing works and discuss possible
future directions.
