Breakdown of the adiabatic Born-Oppenheimer approximation in graphene

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

    Research output: Contribution to journalArticlepeer-review

    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 mechanics. 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) occur. The use of ABO to describe lattice motion in metals is, therefore, questionable. In spite of this, ABO has proved effective for the accurate determination of chemical reactions, molecular dynamics and phonon frequencies in a wide range of metallic systems. Here, we show that ABO fails in graphene. Graphene, recently discovered in the free state, is a zero-bandgap semiconductor that becomes a metal if the Fermi energy is tuned applying a gate voltage, Vg. This induces a stiffening of the Raman G peak that cannot be described within ABO. ©2007 Nature Publishing Group.
    Original languageEnglish
    Pages (from-to)198-201
    Number of pages3
    JournalNature Materials
    Volume6
    Issue number3
    DOIs
    Publication statusPublished - 7 Mar 2007

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