Supercritical instability in graphene with two charged impurities

Abstract

We study the supercritical instability in gapped graphene with two charged impurities separated by distance R using the two-dimensional Dirac equation for electron quasiparticles. Attention is paid to a situation when charges of impurities are subcritical, whereas their total charge exceeds a critical one. The critical distance R_{cr} in the system of two charged centers is defined as that at which the electron bound state with the lowest energy reaches the boundary of the lower continuum. A variational calculation of the critical distance R_{cr} separating the supercritical (R<R_{cr}) and subcritical (R>R_{cr}) regimes is carried out. It is shown that the critical distance R_{cr} increases as the quasiparticle gap decreases. The energy and width of a quasistationary state as functions of the distance between two impurities are derived in the quasiclassical approximation.

12 pages, 1 figure, comments and references added, to match the published version

References in corpus (12)

• Energy Gaps in Graphene Nanoribbons
• Substrate-induced band gap opening in epitaxial graphene
• Quantum interference and Klein tunneling in graphene heterojunctions
• Is graphene in vacuum an insulator?
• The Coulomb impurity problem in graphene
• Vacuum Polarization and Screening of Supercritical Impurities in Graphene
• Observing Atomic Collapse Resonances in Artificial Nuclei on Graphene
• Atomic Collapse and Quasi-Rydberg States in Graphene
• How close can one approach the Dirac point in graphene experimentally?
• Supercritical Coulomb center and excitonic instability in graphene
• Monte-Carlo study of the electron transport properties of monolayer graphene within the tight-binding model
• Effect of topological defects and Coulomb charge on the low energy quantum dynamics of gapped graphene

Cited by in corpus (14)

• Electric dipole induced universality for Dirac fermions in graphene
• Electrons imitating light: Frustrated supercritical collapse in charged arrays on graphene
• Screening of a charged impurity in graphene in a magnetic field
• Electron states in the field of charged impurities in two-dimensional Dirac systems
• Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities
• Excitonic instability of two-dimensional tilted Dirac cones
• Supercriticality of novel type induced by electric dipole in gapped graphene
• Supercritical electric dipole and migration of electron wave function in graphene
• Molecular collapse in monolayer graphene
• Confinement and edge effects on atomic collapse in graphene nanoribbons
• Magnetic Manifestation of Discrete Scaling Symmetry in Dirac Semimetals
• Variational method for the calculation of critical distance between two Coulomb centers in graphene
• Supercritical instability of Dirac electrons in the field of two oppositely charged nuclei
• Electronic and magnetic properties of graphene quantum dots with two charged vacancies