General Argument Supporting Bose-Einstein Condensate Of Dark Excitons In Single And Double Quantum Wells

We show through a novel general field theory argument that for the very same reason that excitons are bright, i.e. emitting photons, they have a higher energy than dark excitons, whatever the carrier spatial configurations is, i.e., even in stressed geometry or for electrons well separated from holes as in a double quantum well structure. Indeed, the same channel which produces the necessary finite electron-hole effective overlap to make them bright, allows for Coulomb interband exchange processes, which are nothing but a sequence of virtual recombination and creation of one electron-hole pair, a fact known in relativistic quantum field theory but never extended to semiconductor physics. The repulsive electron-hole Coulomb exchange interaction, which exists for bright excitons, but not for dark excitons, pushes the bright exciton energy up. If we now remember that dark excitons with spins ± 2 are formed in a natural way through carrier exchange between opposite spin bright excitons, we here predict that in a double quantum well sample with one parabolic trap-a configuration quite appropriate to get a high density-exciton Bose-Einstein condensation should appear, when cooling down the sample, as a dark spot made of (± 2) excitons at the center of the trap. In this paper, we also suggest a possible link between the observed ring structure in a double quantum well and the formation of dark exciton condensate