Speaker
Description
This talk presents a unified view of soliton-induced transparency and supersymmetric confinement in two-dimensional Dirac systems. I first show how the super-Klein tunneling (SKT) effect arises from a correspondence between the Davey–Stewartson II (DS II) integrable system and quasi-exactly solvable Dirac Hamiltonians generated by DS II breather solutions. I then review supersymmetric methods for designing electrostatic potentials that display perfect transmission, localized states, and zero-energy modes. Exactly solvable Lorentzian wells that mimic quantum-dot confinement and radial ring potentials illustrate how supersymmetry organizes degeneracies and exotic current-carrying zero modes. Overall, the framework links integrability, supersymmetry, and perfect transmission in 2D Dirac materials.
