Fermionic bound states in distinct kinklike backgrounds

This work deals with fermions in the background of distinct localized structures in the two-dimensional space-time. Although the structures have a similar topological character, which is responsible for the appearance of fractionally charged excitations, we want to investigate how the geometric deformations that appear in the localized structures contribute to the change in the physical properties of the fermionic bound states. We investigate the two-kink and compact kinklike backgrounds, and we consider two distinct boson-fermion interactions, one motivated by super-symmetry and the other described by the standard Yukawa coupling.