\textit{In situ} Raman Spectroscopy of Suspended Carbon Nanotubes under High Voltage Bias*

We report recent results of Raman spectroscopy taken of individual suspended single-walled carbon nanotubes exhibiting negative differential conductance (NDC) \textit{in situ} under high voltage biases [1]. The transverse and longitudinal optical phonon modes ($G_{+}$ and $G_{-}$ band) are found to respond differently to the applied voltage bias. We observe preferential downshifting of only one optical phonon mode while the other remains largely unchanged, indicating a non-equilibrium phonon population caused by the preferential electron-phonon coupling of only one optical phonon polarization. This preferential coupling is caused by the differences between the two Kohn anomalies in the TO and LO phonon branches [2]. Surprisingly, in most metallic nanotubes, the narrow $G_{+}$ band (TO band) is more strongly heated by electron-phonon scattering at high biases. The non-equilibrium phonon populations produced under high biases are corroborated by anti-Stokes Raman spectroscopy. We correlate the optically measured phonon population to the electrically measured resistivity using a Landauer model to determine key scattering parameters. The electron-phonon scattering mechanism revealed by these measurements and this analysis show the importance of electron-phonon scattering by phonon absorption from the large non-equilibrium phonon population in explaining the observed negative differential conductance [3]. \newline \newline [1] A. W. Bushmaker, V. V. Deshpande , M. W. Bockrath, S. B. Cronin, Direct observation of mode selective electron-phonon coupling in suspended carbon nanotubes, \textit{Nano Lett.}, in press (2007). \newline [2] S. Piscanec, M. Lazzeri, J. Robertson, A. C. Ferrari, F. Mauri, \textit{Phys. Rev. B} \textbf{75}, 35427 (2007). \newline [3] E. Pop, D. Mann, J Cao, Q. Wang, K. Goodson, H. Dai, \textit{Phys. Rev. Lett.} \textbf{95}, 155505 (2005).