# Polarons from first principles, without supercells

## TL;DR

This paper introduces a first-principles computational method to study polarons in insulators and semiconductors without the need for large supercells, enabling accurate analysis of polaron properties.

## Contribution

The authors develop a novel formalism that uses density-functional perturbation theory to study polarons, avoiding supercell limitations and unifying the description of large and small polarons.

## Key findings

- Successfully calculated polaron wavefunctions in LiF and Li2O2.
- Accurately determined polaron formation energies.
- Demonstrated seamless description of large and small polarons.

## Abstract

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 electron-phonon matrix elements from density-functional perturbation theory, in a spirit similar to the Bethe-Salpeter equation for excitons. We show that our approach describes seamlessly large and small polarons, and we illustrate its capability by calculating wavefunctions, formation energies, and spectral decomposition of polarons in LiF and Li2O2.