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- Electron-phonon coupling, vibrational, and optical properties of carbon nanotubes and picotubes
- Phonons and Electron-Phonon Scattering in Carbon Nanotubes
- Doping and phonon renormalization in carbon nanotubes
Electron-phonon coupling, vibrational, and optical properties of carbon nanotubes and picotubes
Huge magnetoresistance by phonon scattering in carbon nanotubes. Huge magnetoresistance by phonon scatter in g in carbon nanotubes. The phonon -mediated resistivity in metallic carbon nanotubes is studied based on a cont in uum model for electrons and. A large magnetoresistance due to the appearance of coupl in g via a deformation potential is predicted in a high.
Keywords: Carbon nanotubes ; Phonon scatter in g ; Magnetoresistance. CNs [3,4]. Phonon scatter in g is another ma in orig in.
In this study, we consider scatter in g. With in a tight-b in d in g model. Calculated magnetoresistance in a low-magnetic-eld. The reduction of scatter in g in magnetic elds. This work was supported in part by Grants- in -Aid. Physica E 6 — www. All rights reserved. PACS: Rj; Di; E-mail address: suzuura issp. PII: S 99 Huge magnetoresistance by phonon scattering in carbon nanotubes READ.
A large magnetoresistance due to the appearance of coupl in g via a deformation potential is predicted in a high magnetic eld. Gd Keywords: Carbon nanotubes ; Phonon scatter in g ; Magnetoresistance 1. Introduction Carbon nanotubes CNs are quasi-one-dimensional materials made of sp 2 -hybridized carbon networks  and one-third of them become metallic see for example, Ref.
Transport properties are particularly in terest in g because of their unique topological structures. The purpose of this paper is to study resistivity of CNs limited by phonon s in magnetic elds. For impurity scatter in g , it was shown theoretically that there is no back scatter in g for impurity potentials with a range larger than the lattice spac in g in metallic CNs [3,4].
Phonon scatter in g is another ma in orig in of the resistivity and gives dom in ant contributions at high temperature. Suzuura ter in g and the change of local band structure causes a small resistivity. A magnetic eld changes the situation drastically and leads to an appreciable amount of back scatter in g due to the deformation potential.
This leads to in crease of the resistivity in a magnetic eld, or positive magnetoresistance , in metallic CNs. In this paper, we shall demonstrate this huge positive magnetoresistance by calculat in g phonon -mediated resistivity us in g the Boltzmann equation under magnetic elds in the high-temperature limit.
In this study, we consider scatter in g by acoustic phonon s with long wavelength and neglect the scatter in g between the two Fermi po in ts. PII: S 99 H. Suzuura, T. A magnetic eld parallel to the axis opens the energy gap in metallic CNs due to the Aharonov—Bohm eect [7,8], giv in g rise to a strong modication of transport, but will not be discussed here. Cyl in drical geometry of CNs makes considerable modications for phonon modes.
In the in nite R limit, this model describes the zone-folded phonon modes of a two-dimensional isotropic elastic media. Therefore, the parameters B and are determ in ed by the sound velocity of transverse and longitud in al acoustic modes in a graphite sheet. It is important that the stra in tensors correctly in clude the coupl in g between in -plane and out-ofplane deformations for nite R. Two zero modes with regards to translations in the direction perpendicular to the tube axis cannot be reproduced unless the radial displacement is in cluded in a correct manner.
Further, a uniform deformation in the radial direction causes in -plane stretch in g which costs nonzero energy in versely proportional to R correspond in g to the appearance of the breath in g mode.
The present model properly describes such characteristic modes in a cyl in drical geometry as well as zone-folded modes of a graphite sheet and shows quite good agreements with the results of a microscopic calculation . In the absence of a magnetic eld, only particular phonon modes contribute to the scatter in g and leads to a resistivity dependent on the chirality of CN at low temperatures .
In magnetic elds, various phonon s take part in the electron scatter in g because of nonuniform distribution of the electron wave function along the circumference. Therefore, the correct phonon model is in dispensable to the calculation of phonon -mediated magnetoresistance.
Strictly speak in g, we should take in to account effects of a curvature deformation which gives the k 2 dispersion to the out-of-plane modes in a graphite sheet, where k is the wave vector. Without such eects the model gives many false zero modes correspond in g to radial deformation without change in the circumference length of CN. There can be an o-diagonal term due to local modication of the band structure caused by acoustic phonon s. With in a tight-b in d in g model this can be described by a deformation of a transfer in tegral between nearest-neighbor sites .
We shall calculate the resistivity in the hightemperature regime where phonon scatter in g is dom in ant and restrict ourselves to the case that the Fermi level is lower than the bottom of the rst excited bands. The electron density is characterized by the Fermi wave number k F. In addition, the energy of absorbed or emitted phonon s is neglected as it is small compared with that of electrons. Under these conditions, the resistivity limited by phonon scatter in g is calculated by the Boltzmann transport equation in a similar way for impurity scatter in g .
This value is not dierent from known values 16—30 in graphite . The upper part of Fig. Electrons are not backscattered at all in the absence of a magnetic eld but this absence of back scatter in g disappears in magnetic elds, lead in g to the huge positive magnetoresistance.
This is understood by the analogy with the scatter in g by the long-range impurity potential . This magnetoresistance decreases with the in crease of the charge dop in g. Resistivity with a xed electron density in magnetic elds. The upper gure shows contributions from the diagonal deformation potential and the lower shows those from the o-diagonal term for each electron density.
Calculated magnetoresistance in a low-magnetic-eld region. With the in crease of the charge dop in g, it starts to exhibit a negative magnetoresistance although its absolute magnitude is smaller than that for the resistivity limited by the diagonal g 1 term. The reduction of scatter in g in magnetic elds for nonzero k F for both g 1 and g 2 is caused by the change of the wave function at nonzero k F result in g in the decrease of overlap between the in itial and nal states [12,16].
The huge positive magnetoresistance predicted here can be observed experimentally in multi-wall CNs. Conclusion We have studied the resistivity of metallic CNs in a magnetic eld. In the absence of charge dop in g, a huge positive magnetoresistance has been predicted because of the magnetically in duced scatter in g by the diagonal deformation potential.
The in crease of charge dop in g reduces the positive magnetoresistance. This phenomenon is experimentally observable in large-radius CNs. References  S. Iijima, Nature Saito, G. Dresselhaus, M. Ando, T. Nakanishi, J. Japan 67 Nakanishi, R.
Saito, J. Ajiki, T. Ando, J. Japan 62 Japan 65 Japan 63 Saito, T. Takeya, T. Kimura, G. Dresselhaus, Phys. B 57 Ando, Molec. Pietronero, S. Strassler, H. Zeller, M. Rice, Phys. B 22 Seri, T. Japan 66 Su, J. Schrieer, A. Heeger, Phys. Seri, J.
Phonons and Electron-Phonon Scattering in Carbon Nanotubes
Acoustic phonons are modeled by applying the elastic continuum model to single wall nanotubes SWNTs with the nanotube approximated as an elastic membrane with cylindrical symmetry. The dispersion relations are compared for various diameter nanotubes. These calculations provide the full set of phonon modes for the SWNTs; this is in contrast to most calculations that consider a subset of these modes. The allowed phonon assisted electronic transitions are considered for intravalley-intrasubband and intravalley-intersubband transitions. Finally, these results indicate that phonon-bottleneck effects should be important for the short nanotubes being considered for nanotube-based devices exhibiting quasi-ballistic transport.
Pop, E. Jacksonville, Florida, USA. August 10—14, The electron-phonon energy dissipation bottleneck is examined in silicon and carbon nanoscale devices. Monte Carlo simulations of Joule heating are used to investigate the spectrum of phonon emission in bulk and strained silicon. The generated phonon distributions are highly non-uniform in energy and momentum, although they can be approximately grouped into one third acoustic AC and two thirds optical phonons OP at high electric fields. The phonon dissipation is markedly different in strained silicon at low electric fields, where certain relaxation mechanisms are blocked by scattering selection rules.
Phonons and electron-phonon scattering in carbon nanotubes. Hidekatsu Suzuura* and Tsuneya Ando*. Institute for Solid State Physics, University of Tokyo.
Doping and phonon renormalization in carbon nanotubes
Physical and Chemical Properties of Carbon Nanotubes. Single-walled carbon nanotube SWCNTs can be thought of as graphene a single graphene sheet wrapped up to form a one-atom-thick cylinders. CNTs were discovered by Iijima [ 1 ] in , since then the excellent charge transport properties of CNTs have been of great interest, for its great potential applications in nanoelectronics, such as high-speed field-effect transistors FETs [ 2 , 3 ], single-electron memories [ 4 ], and chemical sensors [ 5 ]. The band gap of the semiconducting SWCNT is inversely proportional to the tube diameter, which allows such tubes to be used in various different applications. CNTs display outstanding electrical properties such as ballistic transport or diffusive transport with long mean free path, which is of the order of a micrometer.
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Electron-phonon scattering is studied within an effective-mass theory. A continuum model for acoustic phonons is introduced and electron-phonon interaction due to modification of band structure is derived as well as a normal deformation potential. In a metallic nanotube, the deformation potential does not partic-ipate in electron scattering and a metallic nanotube becomes nearly a one-dimensional ballistic conductor even at room temperature. A resistivity determined by small band-structure interaction depends on the chirality at low temperatures. A magnetic field perpendicular to the axis induces electron scattering by the deformation potential, giving rise to huge positive magnetoresistance. Documents: Advanced Search Include Citations. Authors: Advanced Search Include Citations.
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Carbon Nanotubes pp Cite as. The discovery of Novoselov et al. Indeed, recent theoretical studies of graphene reveal that thelinear electronic band dispersion near the Brillouin zone corners gives rise to electronsand holes that propagate as if they were massless fermions and anomalous quantumtransport was experimentally observed.
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