Scattering amplitudes for dark and bright excitons

Using the composite boson many-body formalism that takes single-exciton states rather than free carrier states as a basis, we derive the integral equation fulfilled by the exciton-exciton effective scattering from which the role of fermion exchanges can be unraveled. For excitons made of (+/- 1/2)-spin electrons and (+/- 3/2)-spin holes, as in GaAs heterostructures, one major result is that most spin configurations lead to brightness-conserving scatterings with equal amplitude Delta, despite differences in the carrier exchanges involved. A brightness-changing channel also exists when two opposite-spin excitons scatter: dark excitons ( 2, -2) can end either in the same dark states with an amplitude Delta(e), or in opposite-spin bright states ( 1, -1), with a different amplitude Delta(o), the number of carrier exchanges involved in these scatterings being even or odd, respectively. Another major result is that these amplitudes are linked by a striking relation, Delta(e) + Delta(o) = Delta, which has decisive consequence on exciton Bose-Einstein condensation. By using Born values, we show that the exciton condensate can be optically observed through a bright part when excitons have large dipole only, that is, when the electrons and holes are in two well-separated layers, as in current experiments. Copyright (C) EPLA, 2017