Theory of excitons in colloidal semiconductor nanoplatelets

Semiconductor nanoplatelets---the colloidal analog of quantum wells---exhibit excitonic transitions highly sensitive to their thickness and surface treatment. Here, we present a general theory that describes the underlying physical processes. In particular, we include a less-intuitive effect: how out-of-plane quantum confinement impacts in-plane effective masses. We combine first-principles calculations with models based on $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ theory and the envelope function approximation to show how thickness and surface treatments (ligands or shells) influence excitonic properties. Our results reproduce experiments and provide intuition and quantitative insights on nanoplatelet behavior.