Fermions on Asymmetric Bloch Branes

In this paper we investigate the localization and mass spectrum of fermions on asymmetric Bloch branes generated by two scalars $\phi$ and $\chi$. The internal structure of these branes is very different from other ones. In order to trap fermions on the asymmetric Bloch branes, the couplings with background scalars $\eta\bar{\Psi}F(\phi,\chi)\Psi$ are introduced, where $\eta$ is the coupling constant and $F(\phi,\chi)$ is a function of $\phi$ and $\chi$. We find that the usual couplings $F(\phi,\chi)=\phi+\chi$ and $F(\phi,\chi)=\phi\chi$ considered in the literature do not support the localization of 4-dimensional fermions on the branes. While, for the case $\eta\bar{\Psi}(\chi-\phi)\Psi$, which is turned out to be the kink-fermion coupling corresponding to one-scalar-generated brane scenarios, the zero mode of left-handed fermions is normalizable and can be trapped on one of the branes under the condition $\eta>2 a^2/9 $ with $a$ a parameter appeared in the scalar potential, but the right-handed fermion zero mode is non-normalizable. For the coupling $\bar\Psi\chi^{-2a^2/9}(\chi-\phi)\Psi$, the zero mode of left-handed fermions is normalizable for arbitrary $\eta>0$. Again, there does not exist localized zero mode of right-handed fermions. However, discrete bound massive fermions on the branes are found for large coupling constant.