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Breakdown of the adiabatic Born–Oppenheimer approximation in graphene

Nature Materials volume 6, pages 198–201 (2007)Cite this article

Abstract

The adiabatic Born–Oppenheimer approximation (ABO) has been the standard ansatz to describe the interaction between electrons and nuclei since the early days of quantum mechanics1,2. ABO assumes that the lighter electrons adjust adiabatically to the motion of the heavier nuclei, remaining at any time in their instantaneous ground state. ABO is well justified when the energy gap between ground and excited electronic states is larger than the energy scale of the nuclear motion. In metals, the gap is zero and phenomena beyond ABO (such as phonon-mediated superconductivity or phonon-induced renormalization of the electronic properties) occur3. The use of ABO to describe lattice motion in metals is, therefore, questionable4,5. In spite of this, ABO has proved effective for the accurate determination of chemical reactions6, molecular dynamics7,8 and phonon frequencies9,10,11 in a wide range of metallic systems. Here, we show that ABO fails in graphene. Graphene, recently discovered in the free state12,13, is a zero-bandgap semiconductor14 that becomes a metal if the Fermi energy is tuned applying a gate voltage13,15, Vg. This induces a stiffening of the Raman G peak that cannot be described within ABO.

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Figure 1: Experimental set-up.
Figure 2: Raman G peak of doped graphene.
Figure 3: Schematic π band structure of doped graphene near the high-symmetry K point of the Brillouin zone.

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Acknowledgements

The authors thank P. Kim and A. Pinczuk for useful discussions and for sending us a preprint of ref. 18. A.C.F. acknowledges funding from the Royal Society and The Leverhulme Trust. The calculations were carried out at IDRIS (Orsay).

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Authors and Affiliations

  1. Engineering Department, Cambridge University, Cambridge CB3 0FA, UK

    Simone Pisana, Cinzia Casiraghi & Andrea C. Ferrari

  2. IMPMC, Universités Paris 6 et 7, CNRS, IPGP, 140 rue de Lourmel, 75015 Paris, France

    Michele Lazzeri & Francesco Mauri

  3. Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK

    Kostya S. Novoselov & A. K. Geim

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  1. Simone Pisana
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Correspondence to Andrea C. Ferrari or Francesco Mauri.

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Pisana, S., Lazzeri, M., Casiraghi, C. et al. Breakdown of the adiabatic Born–Oppenheimer approximation in graphene. Nature Mater 6, 198–201 (2007). https://doi.org/10.1038/nmat1846

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