Two-dimensional Dirac operators with general δ-shell interactions supported on a straight line

  title={Two-dimensional Dirac operators with general $\delta$-shell interactions supported on a straight line},
  author={Jussi Behrndt and Markus Holzmann and Matěj Tu{\vs}ek},
  journal={Journal of Physics A: Mathematical and Theoretical},
In this paper the two-dimensional Dirac operator with a general hermitian δ-shell interaction supported on a straight line is introduced as a self-adjoint operator and its spectral properties are investigated in detail. In particular, it is demonstrated that the singularly continuous spectrum is always empty and that by switching a certain δ-shell interaction on, it is possible to generate an eigenvalue in the gap of the spectrum of the free operator or to partially or even fully close the gap… 

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