Two-body problem in graphene

Abstract

We study the problem of two Dirac particles interacting through non-relativistic potentials and confined to a two-dimensional sheet, which is the relevant case for graphene layers. The two-body problem cannot be mapped into that of a single particle, due to the non-trivial coupling between the center-of-mass and the relative coordinates, even in the presence of central potentials. We focus on the case of zero total momentum, which is equivalent to that of a single particle in a Sutherland lattice. We show that zero-energy states induce striking new features such as discontinuities in the relative wave function, for particles interacting through a step potential, and a concentration of relative density near the classical turning point, if particles interact via a Coulomb potential. In the latter case we also find that the two-body system becomes unstable above a critical coupling. These phenomena may have bearing on the nature of strong coupling phases in graphene.

13 pages, 7 figures, final version

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• On the Optical Properties of Excitons in Buckled 2D Materials in an External Electric Field
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• Coulomb impurity under magnetic field in graphene: a semiclassical approach
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• Excitonic Collapse in Semiconducting Transition Metal Dichalcogenides
• Spherical topological-insulator nanoparticles: Quantum size effects and optical transitions
• Metastable electron-electron states in double-layer graphene structures
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• Moving zero-gap Wannier-Mott excitons in graphene
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• Supercriticality of novel type induced by electric dipole in gapped graphene
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• Feshbach-type resonances for two-particle scattering in graphene
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• Universal relations for spin-orbit-coupled Fermi gases in two and three dimensions
• Internal Josephson Oscillations for Distinct Momenta Bose-Einstein Condensates
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• Sommerfeld enhancement factor in two-dimensional Dirac materials
• Theoretical analysis of the density of states of graphene at high magnetic field using Haldane pseudopotentials
• Quasi-bound Electron Pairs in Two-Dimensional Materials with a Mexican-Hat Dispersion
• Electron Interactions in Rashba Materials
• Bound electron pairs formed by the spin-orbit interaction in 2D gated structures
• Electron pairs bound by the spin-orbit interaction in 2D gated Rashba materials with two-band spectrum
• Effective Mass of Bound Electron Pairs in Two-Dimensional Materials with a Gapped Band Spectrum
• Radiative decay of bound electron pairs into unbound interacting electrons in 2D materials with two-band spectrum
• Electron-electron interaction in graphene at finite Fermi energy
• Binding and spontaneous condensation of excitons in narrow-gap carbon nanotubes