Scattering rates and lifetime of exact and boson excitons

Abstract

Although excitons are not exact bosons, they are commonly treated as such provided that their composite nature is included in effective scatterings dressed by exchange. We here \emph{prove} that, \emph{whatever these scatterings are}, they cannot give both the scattering rates $T_{ij}^{-1}$ and the exciton lifetime ${\tau }_0$, correctly: A striking factor 1/2 exists between ${\tau }_0^{-1}$ and the sum of $T_{ij}^{-1}$'s, which originates from the composite nature of excitons, irretrievably lost when they are bosonized. This result, which appears as very disturbing at first, casts major doubts on bosonization for problems dealing with \emph{interacting} excitons.

References in corpus (8)

• Exciton-exciton interaction in quantum wells. Optical properties and energy and spin relaxation
• The Effective Bosonic Hamiltonian for Excitons Reconsidered
• Renormalized Bosonic Interaction of Excitons
• Polarized interacting exciton gas in quantum wells and bulk semiconductors
• Commutation technique for interacting close-to-boson excitons
• Effective Hamiltonian for Excitons with Spin Degrees of Freedom
• Effective bosonic hamiltonian for excitons : a too naive concept
• Density expansion of the energy of N close-to-boson excitons

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• Exciton-phonon interaction calls for a revision of the "exciton" concept
• Many-body effects between unbosonized excitons
• The trion: two electrons plus one hole versus one electron plus one exciton
• Optical spectra of a quantum dot in a microcavity in the nonlinear regime
• Closure relations for composite bosons: difference between polaritons and Wannier or Frenkel excitons
• Photon emission induced by elastic exciton--carrier scattering in semiconductor quantum wells
• How composite bosons really interact
• The exciton many-body theory extended to arbitrary composite bosons
• Fundamental collapse of the exciton-exciton effective scattering
• Effect of fermionic components on trion-electron scattering