Exciton-phonon complexes and optical properties in CdSe nanocrystals

A method to calculate the quantum states of exciton-phonon complexes in semiconductor nanocrystals is presented. The exciton-phonon complexes are built from a basis set made of products of phonon states and electron-hole pairs, which are coupled through the electron-phonon Frohlich interaction, and the electron - hole Coulomb and exchange interactions. In CdSe nanocrystals, the conduction band electrons are described by the effective mass equation, while the holes are represented by the spherical 4 x 4 Baldereschi-Lipari Hamiltonian. It is shown that a flexible and complete electron - hole basis, not limited to the 1s-1S(3/2) octet, is essential to obtain converged eigenvalues and the correct polaron shift to the exciton energy. A study of the spectral properties is presented; in particular, the spectral region which involves the lowest exciton - phonon complex eigenstates is analysed in details. Specifically, the non-adiabatic nature of the exciton - phonon dynamics in the nanocrystals examined is clearly shown by the vibron eigenstates that were obtained.