We briefly review the mechanism of fermion localization on a domain wall(“thick brane”) generated by a topologically nontrivial vacuum configuration of scalar fields. We propose an extension of the scalar field coupling to fermions that endows the fermions with an axial mass. In the case of several flavors and fermion generations, this extension can lead to the appearance of the Standard Model Cabibbo–Kobayashi–Maskawa matrix. We also consider a model with two scalar doublets that ensures an additional mechanism of CP-parity violation.