Exciton-phonon coupling in semiconductor quantum dots: Resonant Raman scattering

Abstract

We study the exciton-phonon coupling in spherical quantum dots (QD's) of cubic semiconductors. Both the Fr\"ohlich and deformation interactions are considered with allowance for all types (LO, ${\mathrm{T}}_{2}\mathrm{O}$, ${\mathrm{T}}_{1}\mathrm{O}$, and SO) of optical phonons. The matrix elements of one-phonon transitions between arbitrary exciton states, as well as the selection rules, are determined. Features of different dynamic and optical effects in QD's, e.g., the Jahn-Teller effect, the vibrational resonances, the multiphonon absorption, and the resonant hyper-Raman scattering, are discussed in brief, whereas the resonant Raman scattering (RRS) is studied in more detail. Analytical expressions of the Raman cross section are obtained. Only the confined LO phonons with angular momentum $l=0$ are found to be active in the RRS due to the Fr\"ohlich interaction, while the deformation coupling gives rise to the Raman bands of LO, ${\mathrm{T}}_{2}\mathrm{O}$, and SO phonons of $l=1$. These conclusions are partly confirmed by the experimental RRS spectra of CuBr nanocrystals in glass, where both the TO and LO phonon bands with comparable intensities are observed.