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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References
Born, M. & Oppenheimer, J. R. Zur quantentheorie der molekeln. Ann. Phys. 84, 457–484 (1927).
Ziman, J. M. Electrons and Phonons (Oxford Univ. Press, Oxford, 1960).
Grimvall, G. The Electron-Phonon Interaction in Metals (North-Holland, Amsterdam, 1981).
Ponosov, Y. S., Bolotin, G. A., Thomsen, C. & Cardona, M. Raman scattering in Os: Nonadiabatic renormalization of the optical phonon self energies. Phys. Status Solidi B 208, 257–269 (1988).
White, J. D., Chen, J., Matsiev, D., Auerbach, D. J. & Wodtke, A. M. Conversion of large-amplitude vibration to electron excitation at a metal surface. Nature 433, 503–505 (2005).
Kroes, G. J., Gross, A., Baerends, E. J., Scheffler, M. & McCormack, D. A. Quantum theory of dissociative chemisorption on metal surfaces. Acc. Chem. Res. 35, 193–200 (2002).
Alfe, D., Gillan, M. J. & Price, G. D. The melting curve of iron at the pressures of the Earth’s core from ab initio calculations. Nature 401, 462–464 (1999).
Walker, B. G., Molteni, C. & Marzari, N. Ab initio molecular dynamics of metal surfaces. J. Phys. Condens. Matter 16, S2575–S2596 (2004).
Chester, G. V. The theory of interaction of electrons with lattice vibrations in metals. Adv. Phys. 10, 357–400 (1961).
Baroni, S., De Gironcoli, S., Dal Corso, A. & Giannozzi, P. Phonons and related crystal properties from density functional perturbation theory. Rev. Mod. Phys. 73, 515–562 (2001).
Savrasov, S. Y. & Savrasov, D. Y. Electron-phonon interactions and related physical properties of metals from linear-response theory. Phys. Rev. B 54, 16487–16501 (1996).
Novoselov, K. S. et al. Two dimensional atomic crystals. Proc. Natl Acad. Sci. USA 102, 10451–10453 (2005).
Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).
Wallace, P. R. The band theory of graphite. Phys. Rev. 71, 622–634 (1947).
Novoselov, K. S. et al. Two dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).
Zhang, Y., Tan, Y. W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).
Ferrari, A. C. et al. Raman spectrum of graphene and graphene layers. Phys. Rev. Lett. 97, 187401 (2006).
Yan, J., Zhang, Y., Kim, P. & Pinczuk, A. Electric field effect tuning of electron-phonon coupling in graphene. Preprint at <http://www.arxiv.org/cond-mat/0612634> (2006).
Tuinstra, F. & Koenig, J. Raman spectrum of graphite. J. Chem. Phys. 53, 1126–1130 (1970).
Piscanec, S., Lazzeri, M., Mauri, F., Ferrari, A. C. & Robertson, J. Kohn anomalies and electron phonon interactions in graphite. Phys. Rev. Lett. 93, 185503 (2004).
Dubay, O. & Kresse, G. Accurate density functional calculations for the phonon dispersion relations of graphite layer and carbon nanotubes. Phys. Rev. B 67, 035401 (2003).
Lazzeri, M., Piscanec, S., Mauri, F., Ferrari, A. C. & Robertson, J. Phonon linewidths and electron-phonon coupling in graphite and nanotubes. Phys. Rev. B 73, 155426 (2006).
Zhang, Y. et al. Landau-level splitting in graphene in high magnetic fields. Phys. Rev. Lett. 96, 136806 (2006).
Moos, G., Gahl, C., Fasel, R., Wolf, M. & Hertel, T. Anisotropy of quasiparticle lifetimes and the role of disorder in graphite from ultrafast time-resolved photoemission spectroscopy. Phys. Rev. Lett. 87, 267402 (2001).
Kampfrath, T., Perfetti, L., Schapper, F., Frischkorn, C. & Wolf, M. Strongly coupled optical phonons in the ultrafast dynamics of electronic energy and current relaxation in graphite. Phys. Rev. Lett. 95, 187403 (2005).
Lazzeri, M. & Mauri, F. Non-adiabatic Kohn-anomaly in a doped graphene monolayer. Phys. Rev. Lett. 97, 266407 (2006).
Ando, T. Anomaly of optical phonon in monolayer graphene. J. Phys. Soc. Jpn. 75, 124701 (2006).
Castro Neto, A. H. & Guinea, F. Electron-phonon coupling and Raman spectroscopy in graphene. Phys. Rev. B 75, 045404 (2007).
Ashcroft, N. W. & Mermin, N. D. Solid State Physics (Saunders College, London, 1976).
Piscanec, S., Lazzeri, M., Robertson, J., Ferrari, A. C. & Mauri, F. Optical phonons in carbon nanotubes: Kohn anomalies, peierls distortions and dynamic effects. Phys. Rev. B 75, 035427 (2007).
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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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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DOI: https://doi.org/10.1038/nmat1846
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