Temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation

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{
  "metadata": {
    "is_last": true, 
    "version": 1, 
    "title": "Temperature dependence of electronic eigenenergies in the adiabatic harmonic approximation", 
    "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"
    ], 
    "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\u2019s 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\u2019s 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 \u03bceV 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.", 
    "license": "Creative Commons Attribution 4.0 International", 
    "references": [
      {
        "url": "https://journals.aps.org/prb/abstract/10.1103/PhysRevB.90.214304", 
        "type": "Journal reference", 
        "citation": "S. Ponc\u00e9, G. Antonius, Y. Gillet, P. Boulanger, J. Laflamme Janssen, A. Marini, M. C\u00f4t\u00e9, and X. Gonze, Phys. Rev. B 90, 214304 (2014)", 
        "comment": "Paper in which the method is described", 
        "doi": "10.1103/PhysRevB.90.214304"
      }
    ], 
    "doi": "10.24435/materialscloud:1n-2d", 
    "conceptrecid": "986", 
    "publication_date": "Aug 20, 2021, 18:06:07", 
    "edited_by": 100, 
    "_oai": {
      "id": "oai:materialscloud.org:987"
    }, 
    "contributors": [
      {
        "affiliations": [
          "European Theoretical Spectroscopy Facility, Institute of Condensed Matter and Nanosciences, Universit\u00e9 catholique de Louvain, Chemin des \u00e9toiles 8, bte L07.03.01, B-1348 Louvain-la-neuve, Belgium"
        ], 
        "email": "samuel.ponce@uclouvain.be", 
        "familyname": "Ponc\u00e9", 
        "givennames": "Samuel"
      }, 
      {
        "affiliations": [
          "D\u00e9partement de Physique, Universit\u00e9 de Montreal, C.P. 6128, Succursale Centre-Ville, Montreal, Canada H3C 3J7"
        ], 
        "familyname": "Antonius", 
        "givennames": "Gabriel"
      }, 
      {
        "affiliations": [
          "European Theoretical Spectroscopy Facility, Institute of Condensed Matter and Nanosciences, Universit\u00e9 catholique de Louvain, Chemin des \u00e9toiles 8, bte L07.03.01, B-1348 Louvain-la-neuve, Belgium"
        ], 
        "familyname": "Gillet", 
        "givennames": "Yannick"
      }, 
      {
        "affiliations": [
          "Institut N\u00e9el, 25 avenue des Martyrs, BP 166, 38042 Grenoble cedex 9, France"
        ], 
        "familyname": "Boulanger", 
        "givennames": "Paul"
      }, 
      {
        "affiliations": [
          "European Theoretical Spectroscopy Facility, Institute of Condensed Matter and Nanosciences, Universit\u00e9 catholique de Louvain, Chemin des \u00e9toiles 8, bte L07.03.01, B-1348 Louvain-la-neuve, Belgium"
        ], 
        "familyname": "Laflamme Janssen", 
        "givennames": "Jonathan"
      }, 
      {
        "affiliations": [
          "Consiglio Nazionale delle Ricerche (CNR), Via Salaria Km 29.3, CP 10, 00016, Monterotondo Stazione, Italy"
        ], 
        "familyname": "Marini", 
        "givennames": "Andrea"
      }, 
      {
        "affiliations": [
          "D\u00e9partement de Physique, Universit\u00e9 de Montreal, C.P. 6128, Succursale Centre-Ville, Montreal, Canada H3C 3J7"
        ], 
        "familyname": "C\u00f4t\u00e9", 
        "givennames": "Michel"
      }, 
      {
        "affiliations": [
          "European Theoretical Spectroscopy Facility, Institute of Condensed Matter and Nanosciences, Universit\u00e9 catholique de Louvain, Chemin des \u00e9toiles 8, bte L07.03.01, B-1348 Louvain-la-neuve, Belgium"
        ], 
        "familyname": "Gonze", 
        "givennames": "Xavier"
      }
    ], 
    "owner": 115, 
    "license_addendum": null, 
    "mcid": "2021.138", 
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    "id": "987", 
    "status": "published"
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  "revision": 4, 
  "updated": "2021-08-20T16:06:07.700144+00:00", 
  "created": "2021-08-17T15:56:57.422786+00:00", 
  "id": "987"
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