Optical phonons in carbon nanotubes: Kohn anomalies, Peierls distortions, and dynamic effects

By S. Piscanec, M. Lazzeri, John Robertson, Andrea C. Ferrari, F. Mauri. 2006

407 citations recorded by the source corpus.

We present a detailed study of the vibrational properties of Single Wall Carbon Nanotubes (SWNTs). The phonon dispersions of SWNTs are strongly shaped by the effects of electron-phonon coupling. We analyze the separate contributions of curvature and confinement. Confinement plays a major role in modifying SWNT phonons and is often more relevant than curvature. Due to their one-dimensional character, metallic tubes are expected to undergo Peierls distortions (PD) at T=0K. At finite temperature, PD are no longer present, but phonons with atomic displacements similar to those of the PD are affected by strong Kohn anomalies (KA). We investigate by Density Functional Theory (DFT) KA and PD in metallic SWNTs with diameters up to 3 nm, in the electronic temperature range from 4K to 3000 K. We then derive a set of simple formulas accounting for all the DFT results. Finally, we prove that the static approach, commonly used for the evaluation of phonon frequencies in solids, fails because of the SWNTs reduced dimensionality. The correct description of KA in metallic SWNTs can be obtained only by using a dynamical approach, beyond the adiabatic Born-Oppenheimer approximation, by taking into account non-adiabatic contributions. Dynamic effects induce significant changes in the occurrence and shape of Kohn anomalies. We show that the SWNT Raman G peak can only be interpreted considering the combined dynamic, curvature and confinement effects. We assign the G+ and G- peaks of metallic SWNTs to TO (circumferential) and LO (axial) modes, respectively, the opposite of semiconducting SWNTs.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/f32d21e1f72bbef85c354f92cd0ec40a1c72b98f

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Citations in the corpus

Raman Spectroscopy in Graphene-Based Systems: Prototypes for Nanoscience and Nanometrology (2012, background): “[48, 49], and the overall consistency with quantum chemistry”
Ultrafast stretched-pulse fiber laser mode-locked by carbon nanotubes (2010, background): “In metallic tubes, the LO mode is affected by a Kohn anomaly (KA) [ 43 , 44], which causes the softening of this phonon [43, 44].”
Raman Spectroscopic Characterization of Graphene (2010, background): “Firstly, G band splitting is a common phenomenon of carbon nanomaterial under strain, such as nanotubes (96, 97).”
Monitoring dopants by Raman scattering in an electrochemically top-gated graphene transistor. (2007, background): “The strong electron–phonon coupling in graphene and metallic nanotubes gives rise to Kohn anomalies in the phonon dispersion”
Development of a universal stress sensor for graphene and carbon fibres (2011, background): “In nanotubes, pure curvature splits the graphene E 2 g mode into two components, one parallel and one perpendicular to the tube axi”
Electron-phonon interactions from first principles (2016, background): “(145) have only been reported in (Lazzeri and Mauri, 2006; Piscanec et al., 2007; Caudal et al., 2007; Saitta et al., 2008; Calandra et al., 2010), using the approximation that the bare vertex g can be replaced by the screened vertex g.”
Free-standing single-walled carbon nanotube/SnO2 anode paper for flexible lithium-ion batteries (2012, background): “20 [33] Piscanec S, Lazzeri M, Robertson J, Ferrari AC, Mauri F.”