Evaluation of polaron transport in solids from first-principles

Polarons are formed in polar or ionic solids, either molecular or crystalline, due to local distortions of the lattice induced by charge carriers. Polaron hopping is the primary mechanism of charge transport in these materials, such as functional ceramic compounds, with applications in photovoltaics, thermoelectrics, two-dimensional electron gas transistors, magnetic sensors, spin valve devices, and memories. Understanding the fundamental physics of polaron hopping is, therefore, of prime technological importance. This article provides a brief physical background of polarons and their hopping mechanism, focusing on first-principles calculations of polaron properties. Herein, we review recent selected studies applying the density functional theory (DFT), and describe the merits and challenges in applying DFT for such calculations, highlighting the need to address both electronic and vibrational aspects. The vibrational component of the polaron is evaluated based on structural and total energy calculations, whereas the electronic component is derived from both total energy and electron density calculations. To address the most compelling challenge of calculating polaron properties using DFT, which is the issue of electron localization, we propose to employ calculations of selected vibrational properties, such as the sound velocity, shear modulus, and Grüneisen parameter, to represent the polaron hopping energy; all of which originate from the stiffness of inter-atomic bonds. Such methodology is expected to be more straightforward than the existing ones, however demands standardization.