Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities

Abstract

We study the physics of Dirac fermions in a gapped graphene monolayer containing two Coulomb impurities. For the case of equal impurity charges, we discuss the ground-state energy using the linear combination of atomic orbitals (LCAO) approach. For opposite charges of the Coulomb centers, an electric dipole potential results at large distances. We provide a nonperturbative analysis of the corresponding low-energy scattering problem.

arXiv comment9 pages, 3 figures

References in corpus (25)

• The electronic properties of graphene
• Topological Insulators
• Cloning of Dirac fermions in graphene superlattices
• Universality in Few-body Systems with Large Scattering Length
• Electron-Electron Interactions in Graphene: Current Status and Perspectives
• Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps
• Gauge fields in graphene
• The Coulomb impurity problem in graphene
• Observing Atomic Collapse Resonances in Artificial Nuclei on Graphene
• Elastic scattering theory and transport in graphene
• Atomic Collapse and Quasi-Rydberg States in Graphene
• Geometry, mechanics and electronics of singular structures and wrinkles in graphene
• Electron Interactions and Gap Opening in Graphene Superlattices
• Mapping Dirac Quasiparticles near a Single Coulomb Impurity on Graphene
• Quantum Anomaly in Molecular Physics
• Analytical solution of the bosonic three-body problem
• Supercritical Coulomb center and excitonic instability in graphene
• Screening Charged Impurities and Lifting the Orbital Degeneracy in Graphene by Populating Landau Levels
• Dirac electron in a Coulomb Field in 2+1 Dimensions
• Electric dipole induced universality for Dirac fermions in graphene
• Supercritical instability in graphene with two charged impurities
• Magnetic scattering of Dirac fermions in topological insulators and graphene
• Dipoles in Graphene Have Infinitely Many Bound States
• Bound States and Supercriticality in Graphene-Based Topological Insulators
• Geometric scaling in the spectrum of an electron captured by a stationary finite dipole

Cited by in corpus (12)

• 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
• Supercritical electric dipole and migration of electron wave function in graphene
• Supercriticality of novel type induced by electric dipole in gapped graphene
• Electrical dipole on gapped graphene: Bound states and atomic collapse
• Molecular collapse in monolayer graphene
• Confinement and edge effects on atomic collapse in graphene nanoribbons
• Critical behavior for point monopole and dipole electric impurities in uniformily and uniaxially strained graphene
• Non-Relativistic and Relativistic Equations for the Kratzer Potential plus a Dipole in 2D Systems
• Molecular collapse in graphene: sublattice symmetry effect
• Exact Solutions for a Quantum Ring with a Dipolar Impurity