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Electronic structure of solids, including vibrational effects : temperature dependence, zero-point motion and spectral functions - Xavier Gonze - Mardi 12 décembre 2017 à 11 h

INSP - UPMC - 4 place Jussieu - 75005 Paris - Barre 22-32, 2e étage, salle 201

Xavier Gonze - Ecole Polytechnique de Louvain

Abstract

Modifications of electronic eigenenergies due to vibrational effects and electron-phonon coupling are sizable in many materials with light atoms. While often neglected, they have been recently computed from first principles using different formalisms, with various advantages and drawbacks. In particular, the perturbation-based Allen-Heine-Cardona (AHC) theory is a powerful framework, that can be considered in the adiabatic or non-adiabatic harmonic approximation. Electron-phonon coupling can be obtained from density-functional perturbation theory (DFPT) or from many-body perturbation theory (MBPT), e.g. the GW approximation. In this presentation, I will provide a brief overview of the concepts and formalisms, and present recent progresses, including : the validation of AHC theory implementation in two different software applications, with an agreed DFPT zero-point motion correction of 0.4 eV for the direct bandgap of diamond [1] the MBPT result for the same material, 40% higher [2] ; the breakdown of the adiabatic AHC theory for infrared-active materials, and fix of this problem in the non-adiabatic AHC theory [3,4], with results for diamond, Si, LiF, AlN, BN, MgO. Other consequences of interactions, visible in angle-resolved photoemission spectroscopy (ARPES) experiments, are broadening of quasi-particle peaks and appearance of sidebands, contained in the electron spectral function. We will consider MgO and LiF and determine their Migdal self energy and spectral function [5]. The spectral function obtained from the Dyson equation makes errors in the weight and energy of the QP peak and the position and weight of the phonon-induced sidebands. Only one phonon satellite appears, with an unphysically large energy difference (larger than the highest phonon energy) with respect to the QP peak. By contrast, the spectral function from a cumulant treatment of the same self energy is physically better, giving a quite accurate QP energy and several satellites approximately spaced by the LO phonon energy. We provide a detailed comparison between the first-principles MgO and LiF results and those of the Frohlich Hamiltonian. Such an analysis applies widely to materials with infra-red active phonons.

[1] S. Poncé, G. Antonius, P. Boulanger, E. Cannuccia, A. Marini, M. Côté and X. Gonze, Computational Materials Science 83, 341 (2014).

[2] G. Antonius, S. Poncé, P. Boulanger, M. Côté and X. Gonze, Phys. Rev. Lett. 112, 215501 (2014).

[3] S. Poncé, Y. Gillet, J. Laflamme Janssen, A. Marini, M. Verstraete and X. Gonze, J. Chem. Phys. 143, 102813 (2015).

[4] G. Antonius, S. Poncé, E. Lantagne-Hurtubise, G. Auclair, X. Gonze and M. Côté, Phys. Rev. B 92, 085137 (2015).

[5] J.-P. Néry, P.B. Allen, G. Antonius, L. Reining, A. Miglio, and X. Gonze arXiv:1710.07594.