General $\delta$-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation

Abstract

In this work we consider the two-dimensional Dirac operator with general local singular interactions supported on a closed curve. A systematic study of the interaction is performed by decomposing it into a linear combination of four elementary interactions: electrostatic, Lorentz scalar, magnetic, and a fourth one which can be absorbed by using unitary transformations. We address the self-adjointness and the spectral description of the underlying Dirac operator, and moreover we describe its approximation by Dirac operators with regular potentials.

References in corpus (12)

• The electronic properties of graphene
• All-graphene integrated circuits via strain engineering
• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• Magnetic Kronig-Penney model for Dirac electrons in single-layer graphene
• On the spectral theory of Gesztesy-Šeba realizations of 1-D Dirac operators with point interactions on a discrete set
• Resolvents of self-adjoint extensions with mixed boundary conditions
• Leaky Quantum Graphs: A Review
• Two-dimensional Dirac operators with singular interactions supported on closed curves
• One-dimensional Dirac operators with zero-range interactions: Spectral, scattering, and topological results
• Self-adjoint Dirac operators on domains in ${\mathbb{R}}^3$
• Approximation of one-dimensional relativistic point interactions by regular potentials revised
• Limiting absorption principle and scattering matrix for Dirac operators with $\delta$-shell interactions

Cited by in corpus (7)

• Spectral Properties of the Dirac Operator coupled with $\delta$-Shell Interactions
• Spectral Analysis of Dirac Operators with delta interactions supported on the boundaries of rough domains
• Two-dimensional Dirac operators with general $\delta$-shell interactions supported on a straight line
• Eigenvalue curves for generalized MIT bag models
• Dirac operator spectrum in tubes and layers with a zigzag type boundary
• On two-dimensional Dirac operators with critical delta-shell interactions
• Dirac-Coulomb Operators with Infinite Mass Boundary Conditions in Sectors