Fermions bounded by kinks of false vacuum models

In this work we address the question of existence of fermion bound-states and zero modes in the background of kinks of models presenting a structure with a false and a true vacuum. These models are important for the description of cosmological and condensed-matter systems. The spectrum of fermion bound-states on the background of kinks of a class of asymmetrical scalar field potentials is analytically obtained and the general validity of the result is argued.