Spectral Transition for Dirac Operators with Electrostatic $$\delta $$ -Shell Potentials Supported on the Straight Line

In this note the two dimensional Dirac operator $$A_\eta $$ with an electrostatic $$\delta $$ -shell interaction of strength $$\eta \in {\mathbb {R}}$$ supported on a straight line is studied. We observe a spectral transition in the sense that for the critical interaction strengths $$\eta =\pm 2$$ the continuous spectrum of $$A_\eta $$ inside the spectral gap of the free Dirac operator $$A_0$$ collapses abruptly to a single point.