Scattering amplitudes for dark and bright excitons

Abstract

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 $(\pm 1/2)$-spin electrons and $(\pm 3/2)$-spin holes, as in GaAs heterostructures, one major result is that most spin configurations lead to brightness-conserving scatterings with equal amplitude $\Delta$, in spite of the fact that they involve different carrier exchanges. 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 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 for exciton Bose-Einstein condensation. Indeed, this relation leads to the conclusion that the exciton condensate can be optically observed through a bright part only when excitons have a large dipole, that is, when the electrons and holes are well separated in two adjacent layers.

8 pages, 4 figures

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Cited by in corpus (2)

• Defect-Driven Superfluid Crossover for Two-Dimensional Dipolar Excitons Trapped at Thermodynamic Equilibrium
• Optical signature of quantum coherence in fully dark exciton condensates