  The inner layers of a neutron star crust, composed of a Coulomb lattice of
neutron rich nuclear clusters immersed in a sea of ``free'' superfluid
neutrons, are closely analogous to periodic condensed matter systems such as
electronic, photonic or phononic crystals. Applying methods from solid state
physics to the neutron star context, we study the transport properties of those
``free'' neutrons for the outermost layers of the inner crust, near the drip
point $\rho_{\rm drip} \sim 4\times 10^{11}$ g.cm$^{-3}$. In particular, we
evaluate the effective neutron mass resulting from Bragg scattering by a band
structure calculation. Comparison is made with the case of electrons in solids.
The observational consequences are briefly discussed.
