  The prototypical exciton model of two interacting Dirac particles in graphene
was analyzed in [1] and it was found that in one of the electron-hole
scattering channels the total kinetic energy vanishes, resulting in a singular
behaviour. 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.
