Location of Repository

Breakdown of the adiabatic Born–Oppenheimer approximation in graphene.

By Simone Pisana, Michele Lazzeri, Cinzia Casiraghi, Kostya S. Novoselov, Andre K. Geim, Andrea C. Ferrari and Francesco Mauri


15 pagesInternational audienceThe Born-Oppenheimer approximation (BO) has proven effective for the accurate determination of chemical reactions, molecular dynamics and phonon frequencies in a wide range of metallic systems. Graphene, recently discovered in the free state, is a zero band-gap semiconductor, which becomes a metal if the Fermi energy is tuned applying a gate-voltage Vg. Graphene electrons near the Fermi energy have twodimensional massless dispersions, described by Dirac cones. Here we show that a change in Vg induces a stiffening of the Raman G peak (i.e. the zone-center E2g optical phonon), which cannot be described within BO. Indeed, the E2g vibrations cause rigid oscillations of the Dirac-cones in the reciprocal space. If the electrons followed adiabatically the Dirac-cone oscillations, no change in the phonon frequency would be observed. Instead, since the electron-momentum relaxation near the Fermi level is much slower than the phonon motion, the electrons do not follow the Dirac-cone displacements. This invalidates BO and results in the observed phonon stiffening. This spectacular failure of BO is quite significant since BO has been the fundamental paradigm to determine crystal vibrations from the early days of quantum mechanics

Topics: [PHYS.COND.CM-MSQHE] Physics [physics]/Condensed Matter [cond-mat]/Mesoscopic Systems and Quantum Hall Effect [cond-mat.mes-hall], [PHYS.COND.CM-MS] Physics [physics]/Condensed Matter [cond-mat]/Materials Science [cond-mat.mtrl-sci]
Publisher: Nature Publishing Group
Year: 2007
DOI identifier: 10.1038/nmat1846
OAI identifier: oai:HAL:hal-00135075v1
Provided by: Hal-Diderot
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • https://hal.archives-ouvertes.... (external link)
  • https://hal.archives-ouvertes.... (external link)
  • https://hal.archives-ouvertes.... (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.