Electron-Phonon Interactions and Charge Transport from First-Principles Calculations: Complex Crystals, Higher Order Coupling, and Steps Toward the Small Polaron Regime

Citation

Lee, Nien-En (2021) Electron-Phonon Interactions and Charge Transport from First-Principles Calculations: Complex Crystals, Higher Order Coupling, and Steps Toward the Small Polaron Regime. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/b040-2y98. https://resolver.caltech.edu/CaltechTHESIS:11252020-093720107

Abstract

Electron-phonon (e-ph) interactions quantify the strength of interplay between charge carriers and lattice vibrations and critically determine the transport properties in materials near room temperature. Depending on the coupling strength, charge carriers can exhibit behaviors ranging from propagating waves extending across crystals to trapped particles localized in space. Therefore, accurately describing e-ph interactions plays a central role in quantitative transport studies on real materials. Over the last few years, first-principles methods combining density functional theory (DFT) and related techniques with the Boltzmann transport equation (BTE) have rapidly risen and reached maturity for investigating transport in various metals, semiconductors, and insulators with weak e-ph coupling. The lowest-order e-ph scattering process can be investigated starting from e-ph interactions from DFT calculations; this first-principles approach provides unambiguous quantitative prediction of transport properties such as the conductivity and mobility in common semiconductors and metals over a wide temperature range without using any empirical parameter. Encouraged by the agreement of the computed transport properties with experiment for many simple materials, this thesis aims to extend the applicability of this first-principles methodology and to further our understanding of microscopic transport mechanisms, especially in the wide temperature window near room temperature where transport is governed by e-ph scattering. We present research that expands the state of the art in three distinct ways, focusing on three research directions we pursue in this work. First, we employ the BTE to calculate the hole carrier mobility of naphthalene, an organic molecular crystal containing 36 atoms in a unit cell, the record largest system for first-principles charge transport calculations to date. The results are in excellent agreement with experiments, demonstrating that transport in some high-mobility organic semiconductors can still be explained within the band theory framework, and show that low-frequency rigid molecular motions control the electrical transport in organic molecular semiconductors in the bandlike regime. The second topic is an attempt to go beyond the lowest-order theory of e-ph interactions and quantify the importance of higher-order e-ph processes. We derive the electron-two-phonon scattering rates using many-body perturbation theory, compute them in GaAs, and quantify their impact on the electron mobility. We show that these next-to-leading order e-ph scattering rates, although smaller than the lowest-order contribution, are not negligible, and can compensate the overestimation of mobility generally made by the lowest-order BTE calculation in weakly-polar semiconductors. In the third part of the thesis, we explore the opposite extreme case in which e-ph interactions are strong and lead to the formation of localized (so-called "polaron") electronic states that become self-trapped by the interactions with the atomic vibrations. We derive a rigorous approach based on canonical transformations to compute the energetics of self-localized (small) polarons in materials with strong e-ph interactions. With the aid of \textit{ab initio} e-ph interactions, we carry out the corresponding numerical calculations to investigate the formation energy of small polaron and determine whether the charge carriers favor localized states over the Bloch waves. Due to the low computational cost of our approach, we are able to apply these calculations to various compounds, focusing on oxides, predicting the presence of small polaron in agreement with experiments in various materials. Our work paves the way to understanding small polaron formation and extending these calculations to predict transport in the polaron hopping mechanism in materials with strong e-ph coupling.

Thesis Files