Excitonic Correlations in the Nonlinear Optical Response of Two-dimensional Semiconductor Microstructures: A Nonequilibrium Green’s Function Approach
Important Coulomb correlations among excitons have been extensively demonstrated in weakly-nonlinear optical measurements on quasi-2D semiconductor structures in the coherent regime. The Dynamics Controlled Truncation (DCT) scheme, a perturbation (in the applied field amplitude) theory within the density matrix formalism, has scored much success in elucidating the correlation structures revealed by these experiments. Practically, however, DCT is ill-suited to treat the incoherent aspects of the electronic or excitonic dynamics, and therefore its range of efficient applications is limited to short times and/or low carrier densities. Traditionally, the most powerful approach to study incoherent effects and correlations in highly excited semiconductors is that of nonequilibrium Green’s functions (NGF). A combination of the insights and technical advantages of DCT and NGF can lead to more comprehensive theories for the nonlinear response of semiconductors. This contribution reviews some of our efforts in this direction.
We work within the NGF formalism. Our first step was a derivation within the NGF formalism of the most studied DCT equations of motion for electrons and holes — that to third order in the applied field. We summarize here the arguments that identify the set of NGF diagrams that constitute this equation and show the vanishing of the remaining diagrams (of the same order). This diagram set is to be included in the construction of higher-order kinetic equations for electrons and holes.
For processes involving predominantly excitons, we have formulated, via standard NGF techniques, a kinetic theory treating the excitons as bosons. The exchange effects due to the excitons’ fermionic constituents are included through a judicious choice of exciton—exciton and exciton-photon couplings so that our effective exciton theory, when reduced to the third order coherent limit, yields formally identical optical responses as the third order electron-hole DCT theory. This effective theory can be applied to study higher order excitonic correlations and dephasing due to exciton—exciton scattering. We give an overview of this theory here.
Fundamental to a theoretical description of excitonic correlations is the exciton—exciton scattering amplitude (T-matrix), which can be (partially) characterized by coherent third order optical measurements. This T-matrix is usually calculated within a truncated exciton basis. We provide some justification of this approximation by comparing the resulting χ (3) signals to a frequency-domain four wave mixing experiment on a quantum well microcavity.
KeywordsProbe Pulse Nonlinear Optical Response Fermion Loop Incoherent Effect Keldysh Contour
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