T-matrix analysis of biexcitonic correlations in the nonlinear optical response of semiconductor quantum wells

R. Takayama, N. H. Kwong, I. Rumyantsev, M. Kuwata-Gonokami, R. Binder

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102 Scopus citations


A detailed numerical analysis of excitom-exciton interactions in semiconductor quantum wells is presented. The theory is based on the dynamics-controlled truncation formalism and evaluated for the case of resonant excitation of 1s-heavy-hole excitons. It is formulated in terms of standard concepts of scattering theory, such as the forward-scattering amplitude (or T-matrix). The numerical diagonalization of the exciton-exciton interaction matrix in the 1s-approximation yields the excitonic T-matrix. We discuss the role of the direct and exchange interaction in the effective two-exciton Hamiltonian, which determines the T-matrix, evaluated within the 1s-subspace, and also analyze the effects of the excitonic wave function overlap matrix. Inclusion of the latter is shown to effectively prevent the 1s-approximation from making the Hamiltonian non-hermitian, but a critical discussion shows that other artefacts may be avoided by not including the overlap matrix. We also present a detailed analysis of the correspondence between the excitonic T-matrix in the 1s-approximation and the well-known T-matrix governing two-particle interactions in two dimensional systems via short-range potentials.

Original languageEnglish (US)
Pages (from-to)445-462
Number of pages18
JournalEuropean Physical Journal B
Issue number4
StatePublished - Feb 2 2002


  • 03.65.Nk Scattering theory
  • 71.35.Gg Exciton-mediated interactions
  • 78.67.De Quantum wells

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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