Electron-Phonon Interaction in Single-Wall Carbon Nanotubes: A Time-Domain Study

Tobias Hertel, Gunnar Moos
2000 Physical Review Letters  
We investigate the electron-phonon ͑e-ph͒ interaction in single-wall carbon nanotube samples at room temperature using femtosecond time-resolved photoemission. By probing electrons from the vicinity of the Fermi level we are able to study the e-ph interaction in the metallic nanotube species only. The observed electron dynamics can be used to calculate e-ph scattering matrix elements for two likely scattering scenarios: forward scattering from twistons and backscattering by longitudinal
more » ... ongitudinal acoustic phonons. The corresponding matrix elements reveal an intrinsically weak e-ph interaction approximately 50% smaller than predicted by tight-binding calculations. PACS numbers: 78.66.Tr, 71.38. + i, 72.15.Lh, 78.47. + p The electron-phonon ͑e-ph͒ interaction in carbon nanotubes gives rise to a variety of phenomena such as the temperature dependence of the electrical conductivity [1], the thermoelectric power [2] , and possibly superconductivity [3] . Electron-phonon interactions can also induce subtle changes in the electronic band structure and open a small band gap at the Fermi level of metallic single-wall carbon nanotubes (SWNTs) [4, 5] . Carbon nanotubes have furthermore been found to sustain very large current densities of 10 7 10 8 A͞cm 2 at room temperature without suffering current induced damage [6, 7] , indicative of weak e-ph interactions that result in ballistic electron transport over long distances. The strength of the e-ph interaction naturally plays a key role in these effects. However, a determination of the corresponding matrix elements from conventional transport studies, for example, is difficult due to the unknown residual resistivity, high contact resistances, the complex current path in SWNT samples of mixed tube types, etc. The intrinsic rate of energy transfer between electrons and lattice, however, should not be influenced by these effects. Here we present a direct measurement of the e-ph energy transfer in SWNTs at room temperature. This energy transfer can be obtained by studying the nonequilibrium electron dynamics after the system has been perturbed by rapid heating of the electrons with a femtosecond laser pulse [8] . By analyzing the dynamics of the electron distribution in the vicinity of the Fermi level we can determine the e-ph interaction in the metallic nanotube species. The resulting matrix elements are found to be considerably smaller than predicted by tight-binding calculations. The sample preparation and experimental setup have been described elsewhere [9, 10] . In short, the buckypaper samples used in this study are produced from commercial SWNT suspension (tubes@rice, Houston, Texas) and contain a mixture of metallic and semiconducting SWNTs, in which the diameter distribution is sharply peaked at 12 Å [11] . Photoelectron spectra are obtained by means of the time-of-flight technique with an energy resolution of about 10 meV. The duration of the visible pump (typically 2.32 eV) and frequency doubled probe pulses was 85 fs. The pump pulse fluence of typically 50 mJ͞cm 2 is about an order of magnitude larger than the probe pulse fluence. For a review of the time-resolved photoemission technique, see Ref. [12] . To ensure reproducibility of the data, the experiments were performed at various spots on each of several different samples. We start the discussion of our results with a calculation of the average density of states (DOS) of the bucky-paper samples. This is obtained by summing up the weighted DOS of all constituent nanotube types as determined by the diameter distribution given in Ref. [11] (we assume that chiral angles are distributed randomly). The DOS of the individual tubes is obtained from the electronic structure of graphene by zone folding its 2D band structure into the 1D Brillouin zone of the nanotubes [13]. The resulting average DOS for a nearest neighbor C-C hopping integral g 0 of 2.6 eV is shown in the top panel of Fig. 1 together with the DOS of the ͑9, 9͒ nanotube-a highly probable metallic species within these samples. The spikes in the average DOS originate from the van Hove singularities of the various tube types. The cluster near 60.27 eV can be assigned to semiconducting nanotubes with an average band gap of about 0.22 3 g 0 0.57 eV. Between these spikes the average DOS is found to be constant since only metallic nanotubes contribute in this energy range. This becomes clearer in the middle panel of Fig. 1 , where the DOS is plotted on an expanded energy scale. As discussed previously [9] , spectral features in the bucky-paper DOS are broadened due to a combination of effects, such as the short lifetime of higher energy electrons and tube-tube interactions. In addition to this, the high sensitivity of photoelectron spectroscopy to the alignment of the band structure of individual tubes with respect to the vacuum level, in combination with possible impurity-or "self"doping induced band shifts, leads to a further smearing of these structures in our spectra. Nevertheless, we expect the photoelectrons from the vicinity of the Fermi level to originate predominantly from metallic nanotubes. The intensity of photoelectrons originating from the immediate vicinity of the Fermi level is primarily determined by the Fermi level DOS and the distribution function 5002 0031-9007͞00͞84(21)͞5002(4)$15.00
doi:10.1103/physrevlett.84.5002 pmid:10990852 fatcat:5xbwrqzzkzan7dngizpmnabhe4