In this paper we investigate the localization of fermions on asymmetric thick branes generated by two scalars φ and Χ. In order to trap fermions on the asymmetric branes with kink-like warp factors, the couplings with the background scalars ηΨ F(Χ, φ)Ψ are introduced, where F(Χ,φ) is a function of φ and Χ. We find that the coupling ηΨ ΧφΨ does not support the localization of four-dimensional fermions on the branes. While, for the case ηΨ ΧΨ + η′ Ψ θ Ψ, which is the kink-fermion coupling corresponding to onescalar- generated brane scenarios, the zero mode of left-handed fermions could be trapped on the branes under some conditions.
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