Spectral transition for Dirac operators with electrostatic $δ$-shell potentials supported on the straight line

Abstract

In this note the two dimensional Dirac operator Aη with an electrostatic δ-shell interaction of strength η ∈ R supported on a straight line is studied. We observe a spectral transition in the sense that for the critical interaction strengths η = ±2 the continuous spectrum of Aη inside the spectral gap of the free Dirac operator A 0 collapses abruptly to a single point.