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arXiv · 2604.14103

Chiral Fermion Localization in Two-Kink Scalar Backgrounds: Tunable Brane Positioning and Universal Divergence at the Single-Kink Limit

H. P. Pinheiro·C. A. S. Almeida
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Abstract

The localization of chiral fermionic zero modes in scalar field backgrounds with domain wall structure is a central mechanism in brane-world scenarios. We investigate this mechanism in a system that provides an effective realization of the $(1+1)$-dimensional Jackiw--Rebbi model, using a two-kink scalar background generated by the deformation method applied to the $φ^4$ model. The two-kink profile introduces two physically distinct parameters: an asymmetry parameter $a_2$ controlling the left-right symmetry of the scalar background, and an inter-kink separation parameter $b$ controlling the distance between the constituent domain walls. We establish two independent scaling laws. First, the collective center-of-mass position of the chiral zero modes responds linearly to $a_2$, providing a mechanism for continuously tuning the effective brane position in the extra dimension. Second, the differential spatial separation between the two chiral modes diverges as the two-kink background collapses into a simple kink, following a power law in $(b-1)$ with exponent statistically consistent with $-1$. These two results are physically independent and each admits a precise interpretation in the language of brane-world scenarios. The mechanism is realized concretely in bilayer graphene under an asymmetric two-kink electrostatic potential, providing a tunable platform for probing extra-dimensional localization physics.

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H. P. Pinheiro, C. A. S. Almeida. 2026-04-15. Chiral Fermion Localization in Two-Kink Scalar Backgrounds: Tunable Brane Positioning and Universal Divergence at the Single-Kink Limit. https://arxiv.org/abs/2604.14103

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