Determining Phonon Density of States in Nanomaterials from Optical Fluorescence*

Thermal transport in nanomaterials have attracted a lot of attention in recent years but measuring thermal transport accurately remains a challenge. While size effects play a great role in influencing thermal transport through ballistic and coherent effects, they also influence the phonon density of states (PDOS). So far, direct measurements of PDOS with neutron scattering is difficult to perform on nanomaterials and Raman scattering is the only experimental technique available to validate a theoretically predicted PDOS from a nanomaterial. Here, we propose and evaluate a numerical technique to obtain PDOS directly from temperature dependent optical lineshape information of a fluorescent nanomaterial. We show that such a technique can be used to resolve distinct PDOS features that are results of geometric confinement. Our numerical technique uses a convex approach which is very efficient and is able resolves complicated PDOS lineshapes compared to earlier techniques of deriving PDOS from specific heat. We believe this technique can enable the development of novel nanomaterial designs for better thermal management and thermoelectrics.