Bi-electron bound states in single- and double-layer graphene nanostructures

摘要

The prototypical exciton model of two interacting Dirac particles in graphene wasudanalysed by Sabio et al, Phys. Rev. B 81, 045428 (2010), and it was found that in oneudof the electron-hole scattering channels the total kinetic energy vanishes, resulting inuda singular behaviour. We show that this singularity can be removed by extendingudthe quasiparticle dispersion, thus breaking the symmetry between upper and lowerudDirac cones. The dynamics of an electron-electron pair are then mapped onto thatudof a single particle with negative mass and anisotropic dispersion. We show that theudinterplay between dispersion and repulsive interaction can result in the formation ofudbound, Cooper-pair-like, metastable states in double-layered hybrid structures. Weudanalyse these states by calculating their binding energies, decay rates into the free-udelectron continuum and semiclassical trajectories.udWe also analyse the problem of bi-electron pairing with the inclusion of the twouddominant many-body effects at zero temperature: screening of the Coulomb interactionudby the Dirac sea, and reduction of the available phase space due to Pauli blocking ofudtransitions into the states below the Fermi level. We show that these effects result inudstrong renormalization of the binding energy, but do not destroy the metastable states.udThus the binding energies are strongly dependent on the chemical potential owing toudthe combined effects of screening and Pauli blocking. Hence, the quasibound resonancesudcan be tuned by electrostatic doping.