Direct observation of Born-Oppenheimer approximation breakdown in carbon nanotubes
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From: Nick on 9 May 2010 17:31 From: http://arxiv.org/ftp/arxiv/papers/0901/0901.2947.pdf Direct observation of Born-Oppenheimer approximation breakdown in carbon nanotubes Adam W. Bushmakerâ¡, Vikram V. Deshpande§, Scott Hsieh§, Marc W. Bockrath§, Stephen B. Croninâ¡* Receipt date: 11/25/2008 â¡ University of Southern California, Department of Electrical Engineering -Electrophysics Los Angeles, CA 90089 § California Institute of Technology, Applied Physics. Pasadena, CA 91125 *Corresponding Author: Stephen Cronin Department of Electrical Engineering, University of Southern California Powell Hall of Engineering PHE 624, Los Angeles, CA 90089-0271 Phone: 213-740-8787 Email: scronin(a)usc.edu Abstract: Raman spectra and electrical conductance of individual, pristine, suspended, metallic single-walled carbon nanotubes are measured under applied gate potentials. The G-band is observed to downshift with small applied gate voltages, with the minima occurring at EF = ±½Ephonon, contrary to adiabatic predictions. A subsequent upshift in the Raman frequency at higher gate voltages results in a âWâ-shaped Raman shift profile that agrees well with a non-adiabatic phonon renormalization model. This behavior constitutes the first experimental confirmation of the theoretically predicted breakdown of the Born-Oppenheimer approximation in individual single walled carbon nanotubes. The Born-Oppenheimer (BO) or adiabatic approximation is widely used to simplify the very complex many-body problem of electrons in solids and molecules1, assuming that electrons equilibrate much faster than the atomic motion of the ionic cores. Without this approximation, most molecular and solid state problems become difficult or impossible to solve analytically. Although the BO approximation is valid in most materials and molecular systems, there are a few situations in which it does not hold, including some low atomic weight compounds2-4 , intercalated graphite5, and graphene6. Clean, defect-free single- walled carbon nanotubes (SWNTs) are systems which can be used to verify fundamental phenomena such as Wigner crystallization7 and spin-orbit coupling8, and are ideal candidates for testing fundamental physical predictions. In nanotubes, the BO approximation is expected to break down because of the relatively short vibrational period of the longitudinal optical (LO) phonon and the relatively long electronic relaxation time9, . This breakdown has been observed in semiconducting nanotube mats9, however, inhomogeneities broaden effects in such systems. The breakdown of the BO approximation can be observed directly in an individual nanotube by studying the LO phonon G-Raman feature of metallic SWNTs (m-SWNTs), which is fundamentally different than that of their semiconducting counterparts11 (sc-SWNT). The G-band is broadened and downshifted (reduced in frequency), an effect arising from coupling to a continuum of electronic states9, 10, 12-18. In other words, the LO phonon mode is damped by the free electrons near the Fermi energy19, 20. This coupling is a Kohn anomaly (KA) and has also been referred to as a weakened Peierlâs-like mechanism. The G- band Raman feature in m-SWNTs is particularly interesting under applied gate voltages (Vg) because of the ability to effectively turn off the Kohn anomaly by shifting the Fermi energy (EF). As this happens, the LO phonon frequency upshifts, due to reduced phonon softening of the extinguished Kohn anomaly. /// Wikipedia provides a reasonably competent description of the BornâOppenheimer approximation: http://en.wikipedia.org/wiki/Born_Oppenheimer "In basic terms, it allows the wavefunction of a molecule to be broken into its electronic and nuclear (vibrational, rotational) components." Separablity of total wavefunction into electronic and nuclear components is commonly used (unconsciously) to "prove" that electronc effects are too small to effect nuclear processes. However, the BO approximation is ONLY an approximation! |