New quantum-mechanical phenomenon in a model of electron-electron interaction in graphene

Abstract

A quantum mechanical model of two interacting electrons in graphene is considered. We concentrate on the case of zero total momentum of the pair. We show that the dynamics of the system is very unusual. Both stationary and time-dependent problems are considered. It is shown that the complete set of the wave functions with definite energy includes the new functions, previously overlooked. The time evolution of the wave packet, corresponding to the scattering problem setup, leads to the appearance of the localized state at large time. The asymptotics of this state is found analytically. We obtain the lower bound of the life time of this state, which is connected with the breakdown of the continuous model on the lattice scale. The estimate of this bound gives one a hope to observe the localized states in the experiment.

10 pages, 2 figures

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Cited by in corpus (9)

• Metastable electron-electron states in double-layer graphene structures
• Two-body problem for two-dimensional electrons in Bernervig-Hughes-Zhang model
• Pair states in one-dimensional Dirac systems
• Zero-energy vortices in Dirac materials
• Two-electron bound states near a Coulomb impurity in gapped graphene
• Feshbach-type resonances for two-particle scattering in graphene
• Quasi-bound Electron Pairs in Two-Dimensional Materials with a Mexican-Hat Dispersion
• 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