Theory of photoluminescence spectral line shapes of semiconductor nanocrystals

Single-molecule photoluminescence (PL) spectroscopy of semiconductor nanocrystals (NCs) reveals the nature of exciton-phonon interactions in NCs. Understanding the narrow line shapes at low temperatures and the significant broadening as temperature increases remains an open problem. Here, we develop an atomistic model to describe the PL spectrum of NCs, accounting for excitonic effects, phonon dispersion relations, and exciton-phonon couplings. We use single-molecule PL measurements on CdSe/CdS core-shell NCs from T=4 to T=290K to validate our model and find that the slightly-asymmetric main peak at low temperatures is comprised of a narrow zero-phonon line (ZPL) and several acoustic phonon sidebands. Furthermore, we identify the distinct CdSe optical modes that give rise to the optical phonon sidebands. As the temperature increases, the spectral width shows a stronger dependence on temperature, which we demonstrated to be correlated with frequency shifts and mode-mixing, reflected as higher-order exciton-phonon couplings (Duschinsky rotations). We also model the PL dependence on core size and shell thickness and provide strategies for the design of NCs with narrow linewidths at elevated temperatures.