The role of orbital shape in polaron formation

<h2>Summary</h2> Polarons can significantly affect the electrical properties of materials. However, the electrostatic interactions between electrons and ions within polarons create complex charge correlations in quantum many-body systems, posing critical challenges for understanding and controlling polaron formation. Here, we introduce a straightforward yet effective descriptor for polaron formation based on Coulomb's law, which quantifies the proportion of the density of states associated with orbitals exhibiting strong electrostatic coupling at the band edge. Compared to conventional approaches that rely on electron-phonon coupling strength, our method offers key advantages by considering atom-electron-scale details and maintaining straightforward efficiency. Significantly, it links the atomic configurations to the control of polaron formation, potentially aiding experimental efforts in material design based on atomic-level details. The generality and validity of this approach are demonstrated through the analysis of a variety of metal oxides.