Optical Determination of Electron-Phonon Coupling in Carbon Nanotubes

Abstract

We report on an optical method to directly measure electron-phonon coupling in carbon nanotubes by correlating the first and second harmonic of the resonant Raman excitation profile. The method is applicable to 1D and 0D systems and is not limited to materials that exhibit photoluminescence. Experimental results for electron-phonon coupling with the radial breathing mode in 5 different nanotubes show coupling strengths from 3-11 meV, depending on chirality. The results are in good agreement with the chirality and diameter dependence calculated by Goupalov et al. PACS: 73.63.Fg, 63.22.+m The intrinsic coupling between the electronic and atomic degrees of freedom is fundamental to many transport and optical properties of condensed matter. Here we examine carbon nanotubes, a prototypical one-dimensional (1D) system under intense study for both fundamental physical properties and potential applications as transistors, sensors and optoelectronic devices. The electron-phonon (e-ph) coupling in carbon nanotubes (CNTs) is a key coupling parameter in the electronic band structure, controls Raman scattering [1], heat and electron conductivity [2], and sets an upper limit to ballistic transport [3,4]. In polar semiconductors, multi-phonon replicas in luminescence have been used to measure the Fröhlich e-ph coupling with longitudinal optical (LO) phonons in good agreement with theory [5,6]. In low dimensional systems, the electron and phonon confinement complicates the situation, with conflicting experimental results [7][8][9][10], and requiring model-dependent interpretation to extract the e-ph interaction. E-ph interactions in CNTs are due to the deformation-potential interaction, generally weaker than Fröhlich interaction in polar materials. Nonetheless, evidence of e-ph coupling in CNTs are observed in photoluminescence phonon replicas [11], the Kohn anomaly manifested in the phonon dispersion and line-widths in metallic nanotubes [12] and temperature dependence of optical transition energies [13,14]. However, direct measurements of e-ph coupling in CNTs are lacking.

Excitonic optical transitions characterized by Raman excitation profiles in single-walled carbon nanotubes

“…Previously, this expression has been used to derive the electron-phonon coupling matrix elements of the RBM [36] and the G modes [37] in SWNTs from their REPs.…”

Ultrafast vibrational motion of carbon nanotubes in different pH environments

“…larger diameter tubes, cannot be explained by the electronphonon coupling since the electron-phonon matrix element of the deformation-potential interaction becomes weak when the diameter of SWNT increases. 28,29 Instead of considering electron-phonon coupling, inhomogeneous damping of the lower frequency RBM plausibly accounts for the shorter dephasing time of the lower RBM than that of the higher RBM. 30 From the considerations above, the reason why the FT intensity enhancement in Fig.…”

“…23 In the present study, RBMs are considered to be coupled with electrons through the optical deformation-potential interaction, 28 i.e., the matrix element ͉M e-ph ͉ of the electronphonon coupling can be described by ͉M e-ph ͉ 2 = ͉a / R t 2 + ͑ b / R t ͒cos 3 ͉ 2 , where a and b are the constants, ͓ =mod͑n − m ,3͔͒ is the chiral index, and is the chiral angle. 20,29 Thus the electron-phonon coupling strength decreases if the diameter of the SWNT ͑R t ͒ increases. Consequently, regarding to the note ͑ii͒ above, the shorter dephasing time of the lower frequency RBM, corresponding to the TABLE I.…”

Electron temperature dependence of the electron-phonon coupling strength in double-wall carbon nanotubes

“…The observed energy bottleneck suggests that only a limited set of the total phonon modes 12, 13 participate in the relaxation of the charge carrier energy. The e-ph coupling strength is highly important, and although it has been extensively investigated in single-wall carbon nanotubes (SWNTs) 4,9,14,15 and graphene, 16 very little is known for double-wall nanotubes (DWNTs).In this letter, we present the temperature dependence of the energy transfer rate G(T e ,T l ) from electrons to the lattice in DWNTs. Using time-resolved two-photon photoemission (TR-TPP) spectroscopy 17 , we record the non-thermal and the thermal evolution of the electron distributions and their subsequent equilibration with phonons.…”

“…The observed energy bottleneck suggests that only a limited set of the total phonon modes 12, 13 participate in the relaxation of the charge carrier energy. The e-ph coupling strength is highly important, and although it has been extensively investigated in single-wall carbon nanotubes (SWNTs) 4,9,14,15 and graphene, 16 very little is known for double-wall nanotubes (DWNTs).…”