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Breakdown of the adiabatic approximation in a doped graphene monolayer and in metallic carbon nanotubes

We compute, from first‐principles, the frequency of the phonons associated to the Raman G‐bands in a graphene monolayer and in metallic nanotubes as a function of the charge doping. In both cases, the frequency displays an important measurable shift in the range of doping reached experimentally. As a consequence, Raman spectroscopy can be used as a direct probe of the doping of these systems. Calculations are done using (i) the adiabatic Born–Oppenheimer approximation and (ii) time‐dependent perturbation theory to explore dynamic effects beyond this approximation. The two approaches provide very different results. The frequency shift of the G‐band in graphene and of the G– in metallic tubes represent remarkable failures of the adiabatic Born–Oppenheimer approximation. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)