Fermion localization on degenerate and critical branes

In this work, we analyze the localization of fermions on degenerate and critical Bloch branes. We find the range of coupling constants of the interaction of fermions with the scalar fields that allow us to have normalizable fermion zero mode localized on the brane on both critical and degenerate Bloch branes. In the case of critical branes, our results agree with those found in (Zhao et al 2010 Class. Quantum Grav. 27 185001). The results on fermion localization on degenerate Bloch branes are new. We also propose a coupling of fermions to the scalar fields which leads to localization of massless fermion on both sides of a double brane.