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Temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation

Samuel Poncé1*, Gabriel Antonius2, Yannick Gillet1, Paul Boulanger3, Jonathan Laflamme Janssen1, Andrea Marini4, Michel Côté2, Xavier Gonze1

1 European Theoretical Spectroscopy Facility, 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 Département de Physique, Université de Montreal, C.P. 6128, Succursale Centre-Ville, Montreal, Canada H3C 3J7

3 Institut Néel, 25 avenue des Martyrs, BP 166, 38042 Grenoble cedex 9, France

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

* Corresponding authors emails: samuel.ponce@uclouvain.be
DOI10.24435/materialscloud:1n-2d [version v1]

Publication date: Aug 20, 2021

How to cite this record

Samuel Poncé, Gabriel Antonius, Yannick Gillet, Paul Boulanger, Jonathan Laflamme Janssen, Andrea Marini, Michel Côté, Xavier Gonze, Temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation, Materials Cloud Archive 2021.138 (2021), doi: 10.24435/materialscloud:1n-2d.

Description

The renormalization of electronic eigenenergies due to electron-phonon interactions (temperature dependence and zero-point motion effect) is important in many materials. We address it in the adiabatic harmonic approximation, based on first principles (e.g., density-functional theory), from different points of view: directly from atomic position fluctuations or, alternatively, from Janak’s theorem generalized to the case where the Helmholtz free energy, including the vibrational entropy, is used. We prove their equivalence, based on the usual form of Janak’s theorem and on the dynamical equation. We then also place the Allen-Heine-Cardona (AHC) theory of the renormalization in a first-principles context. The AHC theory relies on the rigid-ion approximation, and naturally leads to a self-energy (Fan) contribution and a Debye-Waller contribution. Such a splitting can also be done for the complete harmonic adiabatic expression, in which the rigid-ion approximation is not required. A numerical study within the density-functional perturbation theory framework allows us to compare the AHC theory with frozen-phonon calculations, with or without the rigid-ion approximation. For the two different numerical approaches without non-rigid-ion terms, the agreement is better than 7 μeV in the case of diamond, which represent an agreement to five significant digits. The magnitude of the non-rigid-ion terms in this case is also presented, distinguishing specific phonon modes contributions to different electronic eigenenergies.

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Keywords

electron-phonon coupling Diamond zero-point motion renormalization Temperature dependence Allen Heine Cardona theory first principles ab initio Adiabatic harmonic approximation Verification and validation FRS-FNRS CECI FRQNT

Version history:

2021.138 (version v1) [This version] Aug 20, 2021 DOI10.24435/materialscloud:1n-2d