Localization of matter fields on flat fermion brane

Abstract In this paper, we investigate the localization of matter fields on a flat fermion thick brane. To localize scalar and fermion fields within a five-dimensional spacetime, we introduce the Yukawa coupling mechanism. Based on this framework, we study the localization and evolution of the scalar field, as well as the localization of the fermion field on the brane. For scalar fields, various effective potentials can be derived from the variation of the scalar field function $$F(\varPhi )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mo>(</mml:mo> <mml:mi>Φ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> in the coupling function. The flat brane can exhibit an effective potential resembling either a volcano or an infinitely deep potential well. By choosing the appropriate coupling parameters, we can find the localized zero mode and some resonance states. This result is similar to the localization of the fermion field on a background scalar field. Additionally, we employ various resonance states as initial values to further explore the evolution on the brane. For the fermion field, we find that the fermion zero mode cannot be localized on the brane. However, by varying the coupling parameters, we obtain an asymmetric infinitely deep potential well. As the coupling parameters increase, the asymmetry become more pronounced.