Impact of the electron-electron correlation on phonon dispersion: Failure of LDA and GGA DFT functionals in graphene and graphite

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 8, 2008, Pages

  Lazzeri, Michele ^a   Attaccalite, Claudio ^b   Wirtz, Ludger ^c   Mauri, Francesco ^a  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

^b UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^c CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 50849092565     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.081406     Document Type: Article

References (34)

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32. In graphite, at the high-symmetry H point the four π bands are degenerate two by two, Δ 0 being the energy difference. By displacing the atoms according to the Γ E2g phonon, these bands remain degenerate and the energy difference is Δ. In analogy to Eqs. 3 4 we define DΓ2 F̄ = (Δ 2 -Δ 02) / (16 d2). By displacing the atoms according to the K A1′ phonon, the four bands are no longer degenerate, being π (π) the two bands which are up (down) shifted and Δ= π - π. We define DK2 F ̄ = (Δ 2 ̄ -Δ 02) / (8 d2), where Δ 2 ̄ indicates the average between the four possible π -π couples.
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