Two-dimensional Dirac operators with general $\delta$-shell interactions supported on a straight line

Abstract

In this paper the two-dimensional Dirac operator with a general hermitian $\delta$-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 $\delta$-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. This suggests that the studied operators may serve as interesting continuum toy-models for Dirac materials. Finally, approximations by Dirac operators with regular potentials are presented.

3 figures

References in corpus (5)

• All-graphene integrated circuits via strain engineering
• Pseudomagnetic fields and ballistic transport in a suspended graphene sheet
• Scattering by linear defects in graphene: a continuum approach
• Spontaneous edge currents for the Dirac equation in two space dimensions
• Intervalley scattering of graphene massless Dirac fermions at 3-periodic grain boundaries

Cited by in corpus (2)

• Bound States and Resonance Analysis of One-Dimensional Relativistic Parity-Symmetric Two Point Interactions
• On two-dimensional Dirac operators with critical delta-shell interactions