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The European Physical Journal B

The role of the biexciton in a dynamic density matrix theory of the semiconductor band edge

V. M. Axt, A. Stahl

Published Jun 1, 1994• 127 citations
Publisher
DOI
10.1007/bf01316964

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Abstract Four‐wave‐mixing (FWM) experiments using a dynamical density matrix model of the semiconductor band edge are discussed. Higher‐order correlation functions are retained which are neglected in the commonly used RPA treatment leading to the semiconductor Bloch equations. In order to terminate the hierarchy of the equations of motion for the higher‐order density matrices systematically a truncation scheme controlled by orders in the driving field is applied. For any prescribed order n in the exciting field a closed set of equations is obtained from which the dielectric response up to order n can be calculated exactly. In addition it turns out that in a coherently driven system part of the remaining density matrices become redundant and can be eliminated. Four‐wave‐mixing experiments are dominated by third‐order contributions. Applying the above‐described results one ends up with only two functions in this case. These are the excitonic and the biexcitonic transition densities. As an application of our method the example of a GaAs single quantum well is studied. Two pulses with finite lengths are assumed such that both heavy‐and light‐hole excitons are excited. The influence of the biexciton contribution on the polarization properties of the FWM signal is analyzed and compared with experimental results.

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Theory of exciton-exciton interactions with nontrivial electronic bands

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Excitons are bound electron-hole pairs in semiconductors whose interactions influence optical properties and determine their collective behavior and emergent correlated phases. Despite the theoretical and experimental significance of these phenomena, a microscopic theory of exciton-exciton interactions that takes into account the full composite nature of these quasiparticles in systems with an arbitrary single-particle Hamiltonian is lacking. Here, we present a general theory of exciton-exciton interactions that builds upon our previous publication [Physical Review B 113, 155440 (2026)], which applied only to conventional semiconductors with weak band hybridization. By contrast, the theory presented here is valid in virtually any crystalline semiconducting system and can be applied to the study of biexciton formation and correlated excitonic phases in systems where band topology, quantum geometry, and moiré effects play a significant role. In addition to the analytical theory, we also present results in simple systems with flat bands with a nontrivial quantum metric and show that the biexcitonic spectrum differs strongly from that in the case without quantum geometry. Our theory paves the way for accurate quantitative calculations of biexciton spectra and excitonic many-body phases in modern condensed-matter systems.

cond-mat.mes-hallCross-listedarXiv:2610.13246•Oct 12, 2026
Abstract Four‐wave‐mixing (FWM) experiments using a dynamical density matrix model of the semiconductor band edge are discussed. Higher‐order correlation functions are retained which are neglected in the commonly used RPA treatment leading to the semiconductor Bloch equations. In order to terminate the hierarchy of the equations of motion for the higher‐order density matrices systematically a truncation scheme controlled by orders in the driving field is applied. For any prescribed order n in the exciting field a closed set of equations is obtained from which the dielectric response up to order n can be calculated exactly. In addition it turns out that in a coherently driven system part of the remaining density matrices become redundant and can be eliminated. Four‐wave‐mixing experiments are dominated by third‐order contributions. Applying the above‐described results one ends up with only two functions in this case. These are the excitonic and the biexcitonic transition densities. As an application of our method the example of a GaAs single quantum well is studied. Two pulses with finite lengths are assumed such that both heavy‐and light‐hole excitons are excited. The influence of the biexciton contribution on the polarization properties of the FWM signal is analyzed and compared with experimental results.
Excitons are bound electron-hole pairs in semiconductors whose interactions influence optical properties and determine their collective behavior and emergent correlated phases. Despite the theoretical and experimental significance of these phenomena, a microscopic theory of exciton-exciton interactions that takes into account the full composite nature of these quasiparticles in systems with an arbitrary single-particle Hamiltonian is lacking. Here, we present a general theory of exciton-exciton interactions that builds upon our previous publication [Physical Review B 113, 155440 (2026)], which applied only to conventional semiconductors with weak band hybridization. By contrast, the theory presented here is valid in virtually any crystalline semiconducting system and can be applied to the study of biexciton formation and correlated excitonic phases in systems where band topology, quantum geometry, and moiré effects play a significant role. In addition to the analytical theory, we also present results in simple systems with flat bands with a nontrivial quantum metric and show that the biexcitonic spectrum differs strongly from that in the case without quantum geometry. Our theory paves the way for accurate quantitative calculations of biexciton spectra and excitonic many-body phases in modern condensed-matter systems.