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Soliton nature of the super-Klein tunneling effect

Francisco Correa1, Luis Inzunza1, and Olaf Lechtenfeld2

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Phys. Rev. D 113, 105027 – Published 29 May, 2026

DOI: https://doi.org/10.1103/kpxt-v3q7

Abstract

We establish a relationship between the Davey-Stewartson II (DS II) integrable system in (2+1) dimensions and quasiexactly solvable planar interacting Dirac Hamiltonians that exhibit the super-Klein tunneling (SKT) effect. The Dirac interactions are constructed from the real and imaginary parts of breather solutions of the DS II system. In this framework, the SKT effect arises when the energy is tuned to match the constant background of the soliton, while the resulting Dirac Hamiltonians simultaneously support bound states embedded in the continuum. By imposing the SKT boundary conditions, we employ Darboux transformations to construct a general three-parameter family of DS II breather solutions that can be mapped to Dirac Hamiltonians. At the initial soliton time, the corresponding Dirac systems form a massless two-parameter family of Hermitian models with nontrivial electrostatic potentials. As the soliton time evolves, the systems become PT-symmetric and develop a nontrivial imaginary mass term. Finally, when the soliton time is taken to be imaginary, the construction yields Hermitian Dirac systems that lack time-reversal symmetry. In all cases, we identify the emergence of quasisymmetry transformations that preserve the SKT subspace of states while not commuting with the full Hamiltonian.

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Phys. Rev. D 113, 105027– Published 29 May, 2026
  • Received 10 February 2026
  • Accepted 21 April 2026
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