Doped carbon nanotubes as quantum memory devices

Based on the given analysis of the phonon spectrum of single-walled carbon nanotubes, it was suggested that tubes doped with foreign atoms be used as quantum memory devices. The longer decoherence time in such devices is accounted for by the suppression of phonon transition due to a gap observed in the phonon spectrum of carbon nanotubes.     

Specific features of low-frequency vibrational dynamics and low-temperature heat capacity of double-walled carbon nanotubes

A continuous model has been constructed for low-frequency dynamics of a double-walled carbon nanotube. The formation of the low-frequency part of the phonon spectrum of a double-walled nanotube from phonon spectra of its constituent single-walled nanotubes has been considered in the framework of the proposed approach. The influence of the environment on the phonon spectrum of a single double-walled carbon nanotube has been analyzed. A combined method has been proposed for estimating the coefficients of the van der Waals interaction between the walls of the nanotube from the spectroscopic data and the known values of the elastic moduli of graphite. The low-temperature specific heat has been calculated for doublewalled carbon nanotubes, which in the field of applicability of the model (T < 35 K) is substantially less than the sum of specific heats of two individual single-walled nanotubes forming it.     

Contact and phonon scattering effects on quantum transport properties of carbon-nanotube field-effect transistors

We investigated the phonon scattering effects on the transport properties of carbon nanotube devices with micron-order lengths at room temperature, using the time-dependent wave-packet approach based on the Kubo formula within a tight-binding approximation. We studied the scattering effects of both the longitudinal acoustic and the optical phonons on the transport properties. The conductance of semiconducting nanotubes is decreased by the acoustic phonon, instead of the optical phonon. Furthermore, we clarified how the electron mobilities of the devices are affected by the acoustic phonon.     

High-field quasiballistic transport in short carbon nanotubes

Single walled carbon nanotubes with Pd Ohmic contacts and lengths ranging from several microns down to 10 nm are investigated by electron transport experiments and theory. The mean-free path (MFP) for acoustic phonon scattering is estimated to be l(ap) approximately 300 nm, and that for optical phonon scattering is l(op) approximately 15 nm. Transport through very short (approximately 10 nm) nanotubes is free of significant acoustic and optical phonon scattering and thus ballistic and quasiballistic at the low- and high-bias voltage limits, respectively. High currents of up to 70 microA can flow through a short nanotube. Possible mechanisms for the eventual electrical breakdown of short nanotubes at high fields are discussed. The results presented here have important implications to high performance nanotube transistors and interconnects.     

Nonequilibrium Green's function approach to phonon transport in defective carbon nanotubes

We have developed a new theoretical formalism for phonon transport in nanostructures using the nonequilibrium phonon Green's function technique and have applied it to thermal conduction in defective carbon nanotubes. The universal quantization of low-temperature thermal conductance in carbon nanotubes can be observed even in the presence of local structural defects such as vacancies and Stone-Wales defects, since the long wavelength acoustic phonons are not scattered by local defects. At room temperature, however, thermal conductance is critically affected by defect scattering since incident phonons are scattered by localized phonons around the defects. We find a remarkable change from quantum to classical features for the thermal transport through defective carbon nanotubes with increasing temperature.     

Terahertz absorption by electrons and confined acoustic phonons in free-standing quantum wells

The acoustic phonon confinement in a free-standing quantum well (FSQW) results in an acoustic phonon energy quantization. Typical quantization energies are in the terahertz frequency range. Free electrons may absorb electromagnetic waves in this frequency range if they emit or absorb acoustic phonons. Therefore, the terahertz absorption reveals the characteristic features of the acoustic phonon spectrum in free-standing structures. We have calculated the absorption coefficient of an electromagnetic wave by free electrons in a FSQW in the terahertz frequency range. We took into account a time dependent electric field, an exact form of the acoustic phonon spectrum and eigenmodes, and electron interactions with confined acoustic phonons through the deformation potential. We demonstrate numerical results for GaAs FSQW of width 100 Å at low lattice temperatures in the frequency range 0.1-1 THz. The absorption coefficient exhibits several structures at frequencies corresponding to the lowest acoustic phonon modes. These features occur due to absorption of photons by electrons, which is accompanied by the emission of corresponding acoustic phonons.     

Dephasing in gapless carbon nanotubes and nanostrips and the suppression of interference in a quantum interferometer based on them

The phonon dephasing of an electron in a finite carbon nanotube and a nanostrip with a gapless spectrum has been studied. It has been shown that its main mechanism is the interaction with soft phonons whose frequencies correspond to the phonon time of transmission through the nanotube. The derived formulas have been used to analyze the suppression of interference in an interferometer consisting of two nanotubes or nanostrips connecting two-dimensional electron seas. Dephasing because of zero-point and thermal vibrations has been considered.     

Phonon spectrum and group velocities in AlN/GaN/AlN and related heterostructures

We theoretically investigated acoustic phonon spectrum and group velocities in an ultra-thin layer of wurtzite GaN embedded within two AlN cladding layers. The core GaN layer thickness has been chosen on the order of the room-temperature dominant phonon wavelength so that the phonon spectrum in such a structure is strongly modified compared to bulk. We derived equations of motion for different phonon polarizations in the anisotropic medium approximation, which allowed us to include specifics of the wurtzite lattice. Based on our model we calculated phonon density of states and phonon group velocity. Using several other example material systems, it has also been demonstrated that the phonon group velocity in the core layer can be made higher or lower than that in corresponding bulk material by a proper selection of the cladding material and its thickness. Presented results shed new light on the effect of barrier material on the phonon spectrum of heterostructures and can be used for modeling the thermal and electrical properties of such structures.     

Band structure, phonon scattering, and the performance limit of single-walled carbon nanotube transistors

Semiconducting single-walled carbon nanotubes are studied in the diffusive transport regime. The peak mobility is found to scale with the square of the nanotube diameter and inversely with temperature. The maximum conductance, corrected for the contacts, is linear in the diameter and inverse temperature. These results are in good agreement with theoretical predictions for acoustic phonon scattering in combination with the unusual band structure of nanotubes. These measurements set the upper bound for the performance of nanotube transistors operating in the diffusive regime.     

Photo-induced absorption in the pump probe spectroscopy of single-walled carbon nanotubes

Femtosecond pump probe spectroscopy is employed to study the photo-induced absorption feature in the single-walled carbon nanotube transient spectrum. The two advantages of the experiment, a chirality enriched sample and tuning the pump wavelength to the resonance of a specific nanotube species, greatly facilitate the identification of the photo-induced absorption signal of one tube species. It is found that a photo-induced absorption feature is located at one radial breathing mode to the blue side of the E11 state. This finding prompts a new explanation for the origin of the photo-induced absorption: the transition from the ground state to a phonon coupled state near the E ii state. The explanation suggests a superposition mechanism of the photo-bleach and photo-induced absorption signals, which may serve as a key to the interpretation of the complex pump probe transient spectrum of carbon nanotubes. The finding sheds some light on the understanding of the complex non-radiative relaxation process and the electronic structure of single-walled carbon nanotubes.     

Nonlinear dynamics of carbon molecular lattices: Soliton plane waves in graphite layers and supersonic acoustic solitons in nanotubes

The dynamics of solitary plane waves in graphite layers and supersonic acoustic solitons in an ideal single-layer carbon nanotube are numerically studied. It is shown that stable solitary waves exist only in flat graphite layers. In nanotubes, only soliton-like excitations can exist and their supersonic motion is always accompanied by phonon emission. The lifetime of such excitations depends on their energy and on the nanotube radius.     

Phonons in carbon nanotubes

A broad review of the unusual one-dimensional properties of phonons in carbon nanotubes is presented, including phonons in isolated nanotubes and in crystalline arrays of nanotubes in nanotube bundles. The main technique for probing the phonon spectra has been Raman spectroscopy and the many unique and unusual features of the Raman spectra of carbon nanotubes are reviewed. Also included is a brief review of the thermal properties of carbon nanotubes in relation to their unusual phonon dispersion relations and density of states.     

Phonon spectromicroscopy of carbon nanostructures with atomic resolution

The vibrational properties of single-wall carbon nanotubes have been probed locally with atomic-scale resolution by inelastic electron tunneling spectroscopy with a low-temperature scanning tunneling microscope. The high spatial resolution has allowed the unraveling of changes in the local phonon spectrum related to topological defects. We demonstrated that the radial breathing mode is suppressed within tube segments of lengths below approximately 3 nm, and that in the cap region phonon modes characteristic of the fullerene hemisphere are emerging. Phonon spectromicroscopy should lead to a better understanding of the mechanisms that limit the transport of heat or electrical charge inside nanostructured carbon materials.     

Carbon nanostructures as an electromechanical bicontinuum

A two-field model provides a unifying framework for elasticity, lattice dynamics and electromechanical coupling in graphene and carbon nanotubes, describes optical phonons, nontrivial acoustic branches, strain-induced gap opening, gap-induced phonon softening, doping-induced deformations, and even the hexagonal graphenic Brillouin zone, and thus explains and extends a previously disparate accumulation of analytical and computational results.     

Lattice vibrations of armchair carbon nanotubes: phonons,soliton deformations and lattice discreteness effects

Small and large-amplitude elastic deformations of the armchair structure of single-walled carbon nanotubes are investigated with emphasis on the cylindrical geometry. As starting model, we consider a discrete one-dimensional lattice of atoms interacting via a Lennard-Jones type two-body potential. In an expansion scheme using cylindrical coordinates where radial displacements are assumed negligible compared to the angular motions, a sine-lattice Hamiltonian is derived. In the limit of small-amplitude angular displacements, the dispersion spectrum of acoustic phonons is derived and the associate characteristic frequency is given as a function of parameters of the model. In the large-amplitude regime, lattice vibrations give rise to kink-type deformations which move undergoing lattice dispersion and lattice discreteness effects. The dispersion law of the kink motion is obtained and shown to lower the effect of lattice discreteness, giving rise to a vanishing Peierls stress for kink sizes of the order of a few lattice spacings. Implications of the coupling of two armchair structures on the stability of vibrational modes of an individual armchair nanotube are also discussed. A gap of forbidden modes is predicted in the phonon spectrum while the energy needed to create a kink deformation in individual nanotubes is shifted in the presence of a wall-to-wall interaction.Received: 2 August 2004, Published online: 14 December 2004PACS: 81.07.De Nanotubes - 62.30. + d Mechanical and elastic waves-vibrations - 63.22. + m Phonons in low-dimensional nanoscale materials - 63.20.Ry Anharmonic lattices modes     

Nanotube phonon waveguide

We find that the high thermal conductivity of carbon nanotubes remains intact under severe structural deformations while the corresponding electrical resistance and thermoelectric power show compromised responses. Similar robust thermal transport against bending is found for boron nitride nanotubes. Surprisingly, for both systems the phonon mean free path exceeds the characteristic length of structural ripples induced by bending and approaches the theoretical limit set by the radius of curvature. The robustness of heat conduction in nanotubes refines the ultimate limit that is far beyond the reach of ordinary materials.     

Phonon and thermal properties of achiral single wall carbon nanotubes

A detailed theoretical study of the phonon and thermal properties of achiral single wall carbon nanotubes has been carried out using force constant model considering up to third nearest-neighbor interactions. We have calculated the phonon dispersions, density of states, radial breathing modes (RBM) and the specific heats for various zigzag and armchair nanotubes, with radii ranging from 2.8 Å to 11.0 Å. A comparative study of phonon spectrum with measured Raman data reveals that the number of Raman active modes for a tube does not depend on the number of atoms present in the unit cell but on its chirality. Calculated phonon modes at the zone center more or less accurately predicted the Raman active modes. The radial breathing mode is of particular interest as for a specific radius of a nanotube it is found to be independent of its chirality. We have also calculated the variation of RBM and G-band modes for tubes of different radii. RBM shows an inverse dependence on the radius of the tube. Finally, the values of specific heat are calculated for various nanotubes at room temperature and it was found that the specific heat shows an exponential dependence on the diameter of the tube.     

Acoustic phonon engineering in coated cylindrical nanowires

We have theoretically investigated the effect of a coating made of the elastically dissimilar material on the acoustic phonon properties of semiconductor nanowires. It is shown that the acoustic impedance mismatch at the interface between the nanowire and the barrier coating affects dramatically the phonon spectra and group velocities in the nanowires. Coatings made of materials with a small sound velocity lead to compression of the phonon energy spectrum and strong reduction of the phonon group velocities. The coatings made of materials with a high sound velocity have opposite effect. Our calculations reveal substantial re-distribution of the elastic deformations in coated nanowires, which results in modification of the phonon transport properties, and corresponding changes in thermal and electrical conduction. We argue that tuning of the coated nanowire material parameters and the barrier layer thickness can be used for engineering the transport properties in such nanostructures.     

High-energy phonon branches of an individual metallic carbon nanotube

We present excitation-energy dependent Raman measurements between 2.05 and 2.41 eV on the same individual carbon nanotube. We find a change in the Raman frequencies of both the D mode (63 cm(-1)/eV) and the high-energy modes. The observed frequencies of the modes at approximately 1600 cm(-1) as a function of laser-energy map the phonon dispersion relation of a metallic tube near the Gamma point of the Brillouin zone. Our results prove the entire first-order Raman spectrum in single-wall carbon nanotubes to originate from double-resonant scattering. Moreover, we confirm experimentally the phonon softening in metallic tubes by a Peierls-like mechanism.     

Discrete and continuum models for calculating the phonon spectra of carbon nanotubes

The vibration spectrum of perfect carbon nanotubes is studied using a two-parametric potential which includes pairwise and three-particle interatomic interactions. This potential was proposed by Keating and allows one to take into account the elasticity of pairwise interatomic bonds and the elasticity associated with a change in the angle between directional interatomic bonds in covalent crystals. Using the Keating potential, the vibration spectrum of a graphite monolayer is calculated and fitted to the vibration spectrum of crystalline graphite, thereby determining the parameters of the potential. With these parameters, the phonon spectra of perfect monolayer graphite nanotubes are calculated. A continuum model, in which a monolayer nanotube is represented as an elastic cylindrical shell of a finite thickness, is also discussed. Within this model, the vibration spectrum of a nanotube is calculated numerically in the long-wavelength limit as a function of the radius and thickness of the nanotube.