Unified theory of electron-phonon renormalization and phonon-assisted optical absorption

TL;DR

This paper develops a unified theoretical framework for understanding electron-phonon interactions and phonon-assisted optical absorption, connecting various existing theories and predicting new phenomena like sub-gap absorption and Urbach tails.

Contribution

It introduces a comprehensive approach that unifies energy-level renormalization and phonon-assisted absorption, applicable to both molecules and solids, and demonstrates its effectiveness with silicon.

Findings

Unified theory encompasses vibronic effects and electron-phonon interactions.

Predicts sub-gap phonon-assisted absorption and Urbach tail in optical spectra.

Demonstrates semiclassical calculation method with silicon.

Abstract

We present a theory of electronic excitation energies and optical absorption spectra which incorporates energy-level renormalization and phonon-assisted optical absorption within a unified framework. Using time-independent perturbation theory we show how the standard approaches for studying vibronic effects in molecules and those for addressing electron-phonon interactions in solids correspond to slightly different choices for the non-interacting Hamiltonian. Our present approach naturally leads to the Allen-Heine theory of temperature-dependent energy levels, the Franck-Condon principle, the Herzberg-Teller effect and to phonon-assisted optical absorption in indirect band gap materials. In addition, our theory predicts sub-gap phonon-assisted optical absorption in direct gap materials, as well as an exponential edge which we tentatively assign to the Urbach tail. We also consider a semiclassical approach to the calculation of optical absorption spectra which simultaneously captures energy-level renormalization and phonon-assisted transitions and is especially suited to first-principles electronic structure calculations. We demonstrate this approach by calculating the phonon-assisted optical absorption spectrum of bulk silicon.