First-principles Evidence for Intermediate Hole Polarons in ZnO

We performed density functional theory calculations at the hybrid-functional level (HSE06) to investigate the nature of the polaronic states in ZnO. Our calculations confirm that neither small~(i.e., strong coupling) electron nor hole polarons are stable in ZnO, in agreement with previous studies [1]. The binding energy of large polarons~(i.e., weak coupling) was determined by evaluating the renormalization of the band edges due to the zero-point motion of the atoms [2]. However, for intermediate polarons at intermediate coupling strength, the harmonic approximation breaks down, and there is currently no first-principle theory. We use the HSE06 effective masses to calculate the Fr\"ohlich coupling constants~$\alpha$. Feynman's path integral technique then yields an intermediate hole polaron, whose binding energy of 245~meV and associated peaks in the optical absorption spectrum are consistent with infrared reflection absorption spectroscopy.\\[4pt] [1] J. B. Varley {\it et al.}, Phys. Rev. B \textbf{85}, 081109(R)(2012).\\[0pt] [2] G. Antonius {\it et al.}, Phys. Rev. Lett. {\bf 112}, 215501 (2014)