Facile <i>ab initio</i> approach for self-localized polarons from canonical transformations
Nien-En Lee, Hsiao-Yi Chen, Jin-Jian Zhou, Marco Bernardi
Abstract
Electronic states in a crystal can localize due to strong electron-phonon ($e$-ph) interactions, forming so-called small polarons. Methods to predict the formation and energetics of small polarons are either computationally costly or not geared toward quantitative predictions. Here we show a formalism based on canonical transformations to compute the polaron formation energy and wave function using ab initio $e$-ph interactions. Comparison of the calculated polaron and band-edge energies allows us to determine whether charge carriers in a material favor a localized small polaron over a delocalized Bloch state. Due to its low computational cost, our approach enables efficient studies of the formation and energetics of small polarons, as we demonstrate by investigating electron and hole polaron formation in alkali halides and metal oxides and peroxides. We outline refinements of our scheme and extensions to compute transport in the polaron hopping regime.