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Super-Klein tunneling in two-dimensional Lorentzian-type barriers in graphene

Alonso Contreras-Astorga1,*, Francisco Correa2,†, Luis Inzunza2,‡, Vít Jakubský3,§, and Raul Valencia-Torres4,∥

  • *Contact author: alonso.contreras@cinvestav.mx
  • †Contact author: francisco.correa.s@usach.cl
  • ‡Contact author: luis.inzunza@usach.cl
  • §Contact author: jakubsky@ujf.cas.cz
  • ∥Contact author: rvalenciat@ipn.mx
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Phys. Rev. Research 8, 043047 – Published 14 October, 2026

DOI: https://doi.org/10.1103/3cj6-dmj4

Abstract

We introduce a two-dimensional model of spin-1/2 Dirac fermions in graphene subjected to a highly tunable electric field, which exhibits super-Klein tunneling. The electric field can be continuously interpolated between two limiting configurations: a uniform electrostatic Lorentzian barrier with translational invariance and a chain of well-separated electrostatic scatterers. We demonstrate that super-Klein tunneling arises naturally as a direct consequence of the intrinsic connection of the model to free-particle dynamics, a relation that is established through methods of supersymmetric quantum mechanics, which provide an elegant and analytically tractable framework. Besides the mentioned super-Klein tunneling, scale invariance of the model and invisibility of the potential for particles of specific energy are revealed, and possible routes toward experimental realization are discussed.

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References (34)

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Phys. Rev. Research 8, 043047– Published 14 October, 2026
  • Received 12 April 2026
  • Accepted 23 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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