Two-electron bound states near a Coulomb impurity in gapped graphene

Abstract

We formulate and solve the perhaps simplest two-body bound state problem for interacting Dirac fermions in two spatial dimensions. A two-body bound state is predicted for gapped graphene monolayers in the presence of weakly repulsive electron-electron interactions and a Coulomb impurity with charge $Ze>0$, where the most interesting case corresponds to $Z=1$. We introduce a variational Chandrasekhar-Dirac spinor wave function and show the existence of at least one bound state. This state leaves clear signatures accessible by scanning tunneling microscopy. One may thereby obtain direct information about the strength of electron-electron interactions in graphene.

13 pages, 6 figures, final version, accepted for publication in PRB

References in corpus (8)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Boron nitride substrates for high-quality graphene electronics
• Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Electronic properties of graphene: a perspective from scanning tunneling microscopy and magneto-transport
• Supercritical Coulomb center and excitonic instability in graphene
• Artifical atoms in interacting graphene quantum dots

Cited by in corpus (3)

• Pair states in one-dimensional Dirac systems
• Effective Mass of Bound Electron Pairs in Two-Dimensional Materials with a Gapped Band Spectrum
• Electromagnetic coupling and transport in a topological insulator-graphene hetero-structure