Metastable electron-electron states in double-layer graphene structures

The prototypical exciton model of two interacting Dirac particles in graphene was analyzed in J. Sabio et al., Phys. Rev. B 81, 045428 (2010) and it was found that in one of the electron-hole scattering channels the total kinetic energy vanishes, resulting in a singular behavior. We show that this singularity can be removed by extending the quasiparticle dispersion, thus breaking the symmetry between upper and lower Dirac cones. The dynamics of an electron-electron pair are then mapped onto that of a single particle with negative mass and anisotropic dispersion. We show that the interplay between dispersion and repulsive interaction can result in the formation of bound, Cooper-pair-like, metastable states in double-layered hybrid structures.