### Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 445-462 |

Number of pages | 18 |

Journal | European Physical Journal B |

Volume | 25 |

Issue number | 4 |

State | Published - Feb 2 2002 |

### Fingerprint

### Keywords

- 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

### Cite this

*European Physical Journal B*,

*25*(4), 445-462.

**T-matrix analysis of biexcitonic correlations in the nonlinear optical response of semiconductor quantum wells.** / Takayama, R.; Kwong, Nai-Hang; Rumyantsev, I.; Kuwata-Gonokami, M.; Binder, Rudolf.

Research output: Contribution to journal › Article

*European Physical Journal B*, vol. 25, no. 4, pp. 445-462.

}

TY - JOUR

T1 - T-matrix analysis of biexcitonic correlations in the nonlinear optical response of semiconductor quantum wells

AU - Takayama, R.

AU - Kwong, Nai-Hang

AU - Rumyantsev, I.

AU - Kuwata-Gonokami, M.

AU - Binder, Rudolf

PY - 2002/2/2

Y1 - 2002/2/2

N2 - 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.

AB - 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.

KW - 03.65.Nk Scattering theory

KW - 71.35.Gg Exciton-mediated interactions

KW - 78.67.De Quantum wells

UR - http://www.scopus.com/inward/record.url?scp=0000205567&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000205567&partnerID=8YFLogxK

M3 - Article

VL - 25

SP - 445

EP - 462

JO - European Physical Journal B

JF - European Physical Journal B

SN - 1434-6028

IS - 4

ER -