Domain-wall melting and entanglement in free-fermion chains with a band structure

We study the melting of a domain wall in free-fermion chains, where the periodic variation of the hopping amplitudes gives rise to a band structure. It is shown that the entanglement grows logarithmically in time, and the prefactor is proportional to the number of filled bands in the initial state. For a dimerized chain the particle density and current are found to have the same expressions as in the homogeneous case, up to a rescaling of the velocity. The universal contribution to the entropy profile is then doubled, while the non-universal part can be extracted numerically from block-Toeplitz matrices.