Two-dimensional Dirac operators with general δ-shell interactions supported on a straight line
Jussi Behrndt, Markus Holzmann, Matěj Tušek
Abstract
Abstract 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. 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.
Topics & Concepts
Dirac operatorEigenvalues and eigenvectorsDirac (video compression format)Hermitian matrixSpectrum (functional analysis)Operator (biology)Shell (structure)Self-adjoint operatorClifford analysisOperator theoryLine (geometry)MathematicsPhysicsMathematical physicsMathematical analysisQuantum mechanicsGeometryChemistryComposite materialNeutrinoGeneMaterials scienceRepressorTranscription factorBiochemistryHilbert spaceSpectral Theory in Mathematical PhysicsQuantum Mechanics and Non-Hermitian PhysicsTopological Materials and Phenomena