Resonant hyper-Raman scattering in spherical quantum dots

TL;DR

This paper presents a theoretical model for resonant hyper-Raman scattering in spherical quantum dots, analyzing electronic and vibrational interactions, and calculating scattering spectra with respect to quantum dot size and distribution.

Contribution

It introduces a new theoretical framework for hyper-Raman scattering in spherical quantum dots, including explicit expressions and selection rules for exciton and vibrational modes.

Findings

Derived an explicit expression for hyper-Raman scattering efficiency.

Identified key exciton and vibrational modes contributing to scattering.

Calculated resonance profiles and discussed size distribution effects.

Abstract

A theoretical model of resonant hyper-Raman scattering by an ensemble of spherical semiconductor quantum dots has been developed. The electronic intermediate states are described as Wannier-Mott excitons in the framework of the envelope function approximation. The optical polar vibrational modes of the nanocrystallites (vibrons) and their interaction with the electronic system are analized with the help of a continuum model satisfying both the mechanical and electrostatic matching conditions at the interface. An explicit expression for the hyper-Raman scattering efficiency is derived, which is valid for incident two-photon energy close to the exciton resonances. The dipole selection rules for optical transitions and Fr\"ohlich-like exciton-lattice interaction are derived: It is shown that only exciton states with total angular momentum $L=0,1$ and vibrational modes with angular momentum $l_p=1$ contribute to the hyper-Raman scattering process. The associated exciton energies, wavefunctions, and vibron frequencies have been obtained for spherical CdSe zincblende-type nanocrystals, and the corresponding hyper-Raman scattering spectrum and resonance profile are calculated. Their dependence on the dot radius and the influence of the size distribution on them are also discussed.