On the dark nature of exciton Bose-Einstein condensate

TL;DR

This paper explains why dark excitons are energetically favored over bright excitons due to Coulomb exchange interactions, predicting that Bose-Einstein condensation in double quantum wells will manifest as a dark exciton condensate at low temperatures.

Contribution

It reveals the fundamental energy difference between bright and dark excitons caused by Coulomb exchange, and predicts dark exciton BEC in double quantum wells.

Findings

Dark excitons are lower in energy than bright excitons due to Coulomb exchange.

Bose-Einstein condensation should form a dark exciton spot at low temperatures.

Dark exciton condensates are expected in double quantum well traps.

Abstract

We show that for the very same reason that excitons are bright, i.e. coupled to photons, they have a higher energy than dark excitons, even for electrons spatially separated from holes, such as in a double quantum well. Indeed, the same channel which produces the finite electron-hole effective overlap responsible for the absorption and emission of photon allows for Coulomb interband exchange processes, which are nothing but a sequence of virtual recombination and creation of one electron-hole pair. Consequently, this additional repulsive electron-hole Coulomb exchange interaction exists for bright excitons, but not for dark excitons. If we now remember that dark excitons with spins $\pm 2$ are formed in a natural way through carrier exchange between two opposite spin bright excitons, we are led to predict that in a double quantum well sample with one trap -- a configuration appropriate to get high density -- exciton Bose-Einstein condensation should appear when cooling down the sample as a dark spot made of $(\pm 2)$ excitons at the center of the trap.