Band gap renormalization, carrier mobilities, and the electron-phonon self-energy in crystalline naphthalene

TL;DR

This study uses first-principles calculations to analyze electron-phonon interactions in naphthalene crystals, accurately predicting band gap renormalization, carrier mobilities, and satellite bands, aligning well with experimental data.

Contribution

It introduces an efficient computational scheme for electron-phonon self-energy that accurately predicts electronic properties of naphthalene with minimal calculations.

Findings

Predicted a 5 eV band gap at room temperature consistent with experiments.

Calculated temperature-dependent mobilities matching experimental measurements.

Demonstrated that a single self-energy calculation suffices for accurate predictions.

Abstract

Organic molecular crystals are expected to feature appreciable electron-phonon interactions that influence their electronic properties at zero and finite temperature. In this work, we report first-principles calculations and an analysis of the electron-phonon self-energy in naphthalene crystals. We compute the zero-point renormalization and temperature dependence of the fundamental band gap, and the resulting scattering lifetimes of electronic states near the valence- and conduction-band edges employing density functional theory. Further, our calculated phonon renormalization of the $GW$-corrected quasiparticle band structure predicts a fundamental band gap of 5 eV for naphthalene at room temperature, in good agreement with experiments. From our calculated phonon-induced electron lifetimes, we obtain the temperature-dependent mobilities of electrons and holes in good agreement with experimental measurements at room temperatures. Finally, we show that an approximate energy self-consistent computational scheme for the electron-phonon self-energy leads to the prediction of strong satellite bands in the electronic band structure. We find that a single calculation of the self-energy can reproduce the self-consistent results of the band gap renormalization and electrical mobilities for naphthalene, provided that the on-the-mass-shell approximation is used, i.e., if the self-energy is evaluated at the bare eigenvalues.