Breakdown of the adiabatic Born–Oppenheimer approximation in graphene

Abstract

Engineering Department, Cambridge University, 9 JJ Thomson Avenue, Cambridge CB3 0FA,UK IMPMC, Universités Paris 6 et 7, CNRS, IPGP, 140 rue de Lourmel, 75015 Paris, France Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK The Born-Oppenheimer approximation (BO) [1] is the standard ansatz to describe the interaction between electrons and nuclei. BO assumes that the lighter electrons adjust adiabatically to the motion of the heavier nuclei, remaining at any time in their instantaneous ground-state. BO 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 BO (such as phonon-mediated superconductivity or phonon-induced renormalization of the electronic properties) occur [2]. The use of BO to describe lattice motion in metals is, therefore, questionable [3, 4]. In spite of this, BO has proven effective for the accurate determination of chemical reactions [5], molecular dynamics [6, 7] and phonon frequencies [9, 8, 10] in a wide range of metallic systems. Graphene, recently discovered in the free state [11, 12], is a zero band-gap semiconductor [13], which becomes a metal if the Fermi energy is tuned applying a gate-voltage Vg [14, 12]. Graphene electrons near the Fermi energy have twodimensional massless dispersions, described by Dirac cones. Here