https://doi.org/10.1140/epjb/e20020051
T-matrix analysis of biexcitonic correlations in the nonlinear optical response of semiconductor quantum wells
1
Cooperative Excitation Project, ERATO, Japan Science and Technology Corporation,
Optical Sciences Center, University of Arizona, Tucson, AZ 85721, USA
2
Optical Sciences Center, University of Arizona, Tucson, AZ 85721, USA
3
Cooperative Excitation Project, ERATO, Japan Science and Technology Corporation,
Department of Applied Physics,
University of Tokyo,
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
Corresponding author: a takayama@u.arizona.edu
Received:
3
August
2001
Revised:
26
December
2001
Published online: 15 February 2002
A detailed numerical analysis of exciton-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.
PACS: 78.67.De – Quantum wells / 03.65.Nk – Scattering theory / 71.35.Gg – Exciton-mediated interactions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002