Super-Klein tunneling in 2D Lorentzian-type barriers in graphene

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.

💡 Research Summary

In this work the authors develop a analytically tractable model for Dirac fermions in graphene subjected to a highly tunable two‑dimensional electrostatic potential. Starting from the free 1+1‑dimensional Dirac equation, they apply a time‑dependent supersymmetric (SUSY) transformation followed by a Wick rotation to obtain a stationary 2‑dimensional Dirac Hamiltonian

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