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Temperature dependence of the electronic structure of semiconductors and insulators

Samuel Poncé1*, Yannick Gillet1, Jonathan Laflamme Janssen1, Andrea Marini2, Matthieu Verstraete3, Xavier Gonze1

1 European Theoretical Spectroscopy Facility and Institute of Condensed Matter and Nanosciences, Université catholique de Louvain, Chemin des étoiles 8, bte L07.03.01, B-1348 Louvain-la-neuve, Belgium

2 Consiglio Nazionale delle Ricerche (CNR), Via Salaria Km 29.3, CP 10, 00016 Monterotondo Stazione, Italy

3 European Theoretical Spectroscopy Facility and Physique des matériaux et nanostructures, Université de Liège, Allée du 6 Août 17, B-4000 Liège, Belgium

* Corresponding authors emails: samuel.pon@gmail.com
DOI10.24435/materialscloud:cj-c4 [version v1]

Publication date: Aug 20, 2021

How to cite this record

Samuel Poncé, Yannick Gillet, Jonathan Laflamme Janssen, Andrea Marini, Matthieu Verstraete, Xavier Gonze, Temperature dependence of the electronic structure of semiconductors and insulators, Materials Cloud Archive 2021.137 (2021), doi: 10.24435/materialscloud:cj-c4.

Description

The renormalization of electronic eigenenergies due to electron-phonon coupling (temperature dependence and zero-point motion effect) is sizable in many materials with light atoms. This effect, often neglected in ab initio calculations, can be computed using the perturbation-based Allen-Heine-Cardona theory in the adiabatic or non-adiabatic harmonic approximation. After a short description of the recent progresses in this field and a brief overview of the theory, we focus on the issue of phonon wavevector sampling convergence, until now poorly understood. Indeed, the renormalization is obtained numerically through a slowly converging q-point integration. For non-zero Born effective charges, we show that a divergence appears in the electron-phonon matrix elements at q → Γ, leading to a divergence of the adiabatic renormalization at band extrema. This problem is exacerbated by the slow convergence of Born effective charges with electronic wavevector sampling, which leaves residual Born effective charges in ab initio calculations on materials that are physically devoid of such charges. Here, we propose a solution that improves this convergence. However, for materials where Born effective charges are physically non-zero, the divergence of the renormalization indicates a breakdown of the adiabatic harmonic approximation, which we assess here by switching to the non-adiabatic harmonic approximation. Also, we study the convergence behavior of the renormalization and develop reliable extrapolation schemes to obtain the converged results. Finally, the adiabatic and non-adiabatic theories, with corrections for the slow Born effective charge convergence problem (and the associated divergence) are applied to the study of five semiconductors and insulators: α-AlN, β-AlN, BN, diamond, and silicon. For these five materials, we present the zero-point renormalization, temperature dependence, phonon-induced lifetime broadening, and the renormalized electronic band structure.

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Keywords

electron-phonon coupling temperature dependence Allen-Heine-Cardona Zero point renormalization ab initio first principles

Version history:

2021.137 (version v1) [This version] Aug 20, 2021 DOI10.24435/materialscloud:cj-c4