Spectral Transition for Dirac Operators with Electrostatic δ -Shell Potentials Supported on the Straight Line

In this note the two dimensional Dirac operator A_η 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 A_η inside the spectral gap of the free Dirac operator A_0 collapses abruptly to a single point.