One-dimensional Coulomb problem in Dirac materials

Abstract

We investigate the one-dimensional Coulomb potential with application to a class of quasirelativistic systems, so-called Dirac-Weyl materials, described by matrix Hamiltonians. We obtain the exact solution of the shifted and truncated Coulomb problems, with the wavefunctions expressed in terms of special functions (namely Whittaker functions), whilst the energy spectrum must be determined via solutions to transcendental equations. Most notably, there are critical bandgaps below which certain low-lying quantum states are missing in a manifestation of atomic collapse.

7 pages, 5 figures

References in corpus (8)

• The electronic properties of graphene
• Electronic States of Graphene Nanoribbons
• Dirac materials
• Selective transmission of Dirac electrons and ballistic magnetoresistance of \textit{n-p} junctions in graphene
• Vacuum Polarization and Screening of Supercritical Impurities in Graphene
• Atomic Collapse and Quasi-Rydberg States in Graphene
• Semiclassical theory of potential scattering for massless Dirac fermions
• Qualitative analysis of trapped Dirac fermions in graphene

Cited by in corpus (5)

• Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields
• Magnetic quantum dots and rings in two dimensions
• General Green's function formalism for layered systems: Wave function approach
• Zitterbewegung and symmetry switching in Klein's four-group
• Excitonic physics in a Dirac quantum dot