Supercritical electric dipole and migration of electron wave function in graphene

Abstract

We study the Dirac equation for quasiparticles in gapped graphene with two oppositely charged impurities by using the technique of linear combination of atomic orbitals and variational Galerkin--Kantorovich method. We show that for sufficiently large charges of impurities the wave function of the occupied electron bound state of the highest energy changes its localization from the negatively charged impurity to the positively charged one as the distance between the impurities increases. This migration of the electron wave function of supercritical electric dipole is a generalization of the familiar phenomenon of the atomic collapse of single charged impurity to the case where electron-hole pairs are spontaneously created from vacuum in bound states with charge impurities thus partially screening them.

8 pages, 6 Figures, and video; submitted to Europhysics Letters

References in corpus (7)

• 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
• Screening of a hypercritical charge in graphene
• Supercritical Coulomb center and excitonic instability in graphene
• Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities

Cited by in corpus (11)

• Screening of a charged impurity in graphene in a magnetic field
• Electron states in the field of charged impurities in two-dimensional Dirac systems
• Supercriticality of novel type induced by electric dipole in gapped graphene
• Molecular collapse in monolayer graphene
• Electrical dipole on gapped graphene: Bound states and atomic collapse
• Confinement and edge effects on atomic collapse in graphene nanoribbons
• The relativistic dynamics of oppositely charged two fermions interacting with external uniform magnetic field
• Critical behavior for point monopole and dipole electric impurities in uniformily and uniaxially strained graphene
• Bound states of a one-dimensional Dirac equation with multiple delta-potentials
• Tunable circular dipolelike system in graphene: Mixed electron-hole states
• Supercritical instability of Dirac electrons in the field of two oppositely charged nuclei