  We investigate the energy band structure of the superfluid flow of ultracold
dilute Fermi gases in a one-dimensional optical lattice along the BCS to BEC
crossover within a mean-field approach. In each side of the crossover region, a
loop structure (swallowtail) appears in the Bloch energy band of the superfluid
above a critical value of the interaction strength. The width of the
swallowtail is largest near unitarity. Across the critical value of the
interaction strength, the profiles of density and pairing field change more
drastically in the BCS side than in the BEC side. It is found that along with
the appearance of the swallowtail, there exists a narrow band in the
quasiparticle energy spectrum close to the chemical potential and the
incompressibility of the Fermi gas consequently experiences a profound dip in
the BCS side, unlike in the BEC side.
