Fermion localization on two-field thick branes

In a recent paper published in this journal, Almeida and collaborators [Phys. Rev. D \textbf{79}, 125022 (2009)] analyze the issue of fermion localization of fermions on a brane constructed from two scalar fields coupled with gravity (Bloch brane model). In this meritorious research the simplest Yukawa coupling $\eta\bar{\Psi}\phi\chi\Psi$ was considered. In that work does not analyze the zero mode in details. In this paper, the localization of fermions on two-field thick branes is reinvestigated. It is found that the simplest Yukawa coupling does not support the localization of fermions on the brane. In addition, the problem of fermion localization for some other Yukawa couplings are analyzed. It is shown that the zero mode for left-handed and right-handed fermions can be localized on the brane depending on the values for the coupling constant $\eta$ and the Bloch brane's parameter $a$.