The soliton nature of the super-Klein tunneling effect

TL;DR

This paper explores the connection between integrable DS II systems and Dirac Hamiltonians exhibiting super-Klein tunneling, revealing how soliton solutions influence the spectral and symmetry properties of these quantum models.

Contribution

It establishes a novel link between integrable soliton systems and Dirac Hamiltonians with super-Klein tunneling, introducing a method to construct these models from DS II breather solutions.

Findings

Constructed a family of Dirac Hamiltonians from DS II breather solutions.

Identified how soliton evolution affects the Hamiltonian's symmetry properties.

Demonstrated the emergence of quasi-symmetries preserving SKT states.

Abstract

We establish a relationship between the Davey--Stewartson II (DS II) integrable system in $(2{+}1)$ dimensions and quasi-exactly 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 $\mathcal{PT}$-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 quasi-symmetry transformations that preserve the SKT subspace of states while not commuting with the full Hamiltonian.