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We develop a formalism and a computational method to study polarons in insulators and semi-conductors from first principles. Unlike in standard calculations requiring large supercells, we solve a secular equation involving phonons and…

We develop a theoretical and computational framework to study polarons in semiconductors and insulators from first principles. Our approach provides the formation energy, excitation energy, and wavefunction of both electron and hole…

This article reviews recent theoretical developments in the ab initio study of polarons in materials. The polaron is an emergent quasiparticle that arises from the interaction between electrons and phonons in solids, and consists of an…

We present a density functional theory (DFT) based supercell approach for modeling small polarons with proper account for the long-range elastic response of the material. Our analysis of the supercell dependence of the polaron properties…

Describing electron-phonon interactions in a solid requires knowledge of the electron-phonon matrix elements in the Hamiltonian. State-of-the-art first-principles calculations for the electron-phonon interaction are limited to the…

Excitons are neutral excitations that are composed of electrons and holes bound together by their attractive Coulomb interaction. The electron and the hole forming the exciton also interact with the underlying atomic lattice, and this…

First-principles calculations combining density functional theory and many-body perturbation theory can provide microscopic insight into the dynamics of electrons and phonons in materials. We review this theoretical and computational…

Polarons can naturally form in materials from the interaction of extra charge carriers with the atomic lattice. Ubiquitous, they are central to various topics and phenomena such as high-T$_c$ superconductivity, electrochromism,…

The behavior of charge carriers in polar materials is governed by electron-phonon interactions, which affect their mobilities via phonon scattering and may localize carriers into self-induced deformation fields, forming self-trapped…

The formation of polarons is a pervasive phenomenon in transition metal oxide compounds, with a strong impact on the physical properties and functionalities of the hosting materials. In its original formulation the polaron problem considers…

A conduction electron (or hole) together with its self-induced polarisation in a polar semiconductor or an ionic crystal forms a quasi-particle, which is called a polaron. The polaron concept is of interest, not only because it describes…

This article reviews the theory of electron-phonon interactions in solids from the point of view of ab-initio calculations. While the electron-phonon interaction has been studied for almost a century, predictive non-empirical calculations…

The electron self-interaction problem in density functional theory affects the accurate modeling of polarons, particularly their localization and formation energy. Charged and neutral density functional formulations have been developed to…

In materials with strong electron-phonon (e-ph) interactions, charge carriers can distort the surrounding lattice and become trapped, forming self-localized (small) polarons. We recently developed an ab initio approach based on canonical…

Electron-phonon interactions in solids are crucial for understanding many interesting phenomena, such as conventional superconductivity, temperature-dependent band-gap renormalization, and polarons. For harmonic materials, the linear…

We present a theoretical framework to describe polarons from first principles within a many-body Green's function formalism. Starting from a general electron-phonon Hamiltonian, we derive a self-consistent Dyson equation in which the…

The quest for topological superconductors triggers revived interests in resolving non-s-wave pairing channels mediated by phonons. While density functional theory and density functional perturbtaion theory have established a powerful…

Polarons, quasiparticles formed through interactions between lattice and charge carriers (electrons and holes), strongly influence the electronic and optical properties of functional materials. In nanostructured BiVO$_{4}$, polaron…

First-principles phonon calculations have been widely performed for studying vibrational properties of condensed matter, where the dynamical matrix is commonly constructed via supercell force-constant calculations or the linear response…

The properties of an electron in a typical solid are modified by the interaction with the crystal ions, leading to the formation of a quasiparticle: the polaron. Such polarons are often described using the Fr\"ohlich Hamiltonian, which…