Gregory Ya. Slepyan

Signal Propagation in Carbon Nanotubes of Arbitrary Chirality

In carbon nanotubes (CNTs) with large radii, either metallic or semiconducting, several subbands contribute to the electrical conduction, while in metallic nonarmchair nanotubes with small radii the wall curvature induces a large energy gap. In this paper, we propose a model for the signal propagation along single wall CNTs (SWCNTs) of arbitrary chirality, at microwave through terahertz frequencies, which takes into account both these characteristics in a self-consistent way. We first study an SWCNT, disregarding the wall curvature, in the frame of a semiclassical treatment based on the Boltzmann equation in the momentum-independent relaxation time approximation. It allows expressing the longitudinal dynamic conductivity in terms of the number of effective conducting channels. Next, we study the behavior of this number as the nanotube radius varies and its relation with the kinetic inductance and quantum capacitance. Furthermore, we show that the effects of the spatial dispersion are negligible in the collision dominated regimes, whereas they may be important in the collisionless regimes, giving rise to sound waves propagating with the Fermi velocity. Then, we study the effects on the electron transport of the terahertz quantum transition induced by the wall curvature by using a quantum kinetic approach. The nanotube curvature modifies the kinetic inductance and gives arise to an additional RLC branch in the equivalent circuit, related to the terahertz quantum transition. The proposed model can be used effectively for analyzing the signal propagation in complex structures composed of SWCNTs with different chirality, such as bundles of SWCNTs and multiwall CNTs, providing that the tunneling between adjacent shells may be disregarded.

Effective medium theory of the microwave and the infrared properties of composites with carbon nanotube inclusions

Abstract Carbon nanotubes (CNs) are electrically small particles at infrared and microwave frequencies. The Mossotti–Clausius formalism for estimating the effective permittivity dyadic of a dilute composite containing CN inclusions is described, and simplifications for certain orientational statistics are discussed. The polarizability dyadic of an electrically small CN is estimated from that of an infinitely long CN of the same cross-sectional diameter. A collection of randomly dispersed, aligned, nonchiral, electrically small CNs is shown to be transparent in the axial direction, but it can be either opaque or transparent in the transverse plane. Its effective electromagnetic response properties can be manipulated by a biasing magnetic field.

Transmission-Line Model for Multiwall Carbon Nanotubes With Intershell Tunneling

The electromagnetic behavior of multiwall carbon nanotubes (MWCNTs), in the frequency range where only intraband transitions are allowed, depends on the combinations of different aspects: the number of effective conducting channels of each shell, the electron tunneling between adjacent shells, and the electromagnetic interaction between shells and the environment. This paper proposes a general transmission-line (TL) model for describing the propagation of electric signals along MWCNTs at microwave through terahertz frequencies that takes into account all these aspects. The dependence of the number of conducting channels of the single shell on the shell chirality and radius is described in the framework of the quasi-classical transport theory. The description of the intershell tunneling effects on the longitudinal transport of the π-electrons is carried on the basis of the density matrix formalism and Liouvilles equation. The electromagnetic coupling between the shells and ground plane is described in the frame of the classical TL theory. The intershell tunneling qualitatively changes the form of the TL equations through the tunneling inductance and capacitance operators, which have to be added, respectively, in series to the (kinetic and magnetic) inductance matrix and in parallel to the (quantum and electrical) capacitance matrix. For carbon nanotube (CNT) lengths greater than 500 nm, the norm of the tunneling inductance operator is greater than 60% of the norm of the total inductance in the frequency range from gigahertz to terahertz. The tunneling inductance is responsible for a considerable coupling between the shells and gives rise to strong spatial dispersion. The model has been used to analyze the eigenmodes of a double-wall CNT above a ground plane. The intershell tunneling gives arise to strong anomalous dispersion in antisymmetrical modes.

Effects of inclusion dimensions and p-type doping in the terahertz spectra of composite materials containing bundles of single-wall carbon nanotubes

Experiments recently showed that the finite lengths of single-wall carbon nanotubes (SWNTs) randomly dispersed and randomly aligned in a composite material are responsible for the appearance of a broad peak in its terahertz conductivity. We investigated, both theoretically and experimentally, the influences of the cross-sectional diameter and the acid-induced p-type doping of SWNT bundles in composite materials on their terahertz conductivity peaks (TCPs). We found that the TCP blue-shifts if the inclusion diameter is larger, and that doping enhances the effective conductivity of the composite material. But, a theoretical prediction of the blue-shifting of the TCP by p-type doping was only weakly supported by experimental evidence. All experimental observations turned out to be in good qualitative agreement with the concept of localized plasmon resonance in SWNTs.

Terahertz sensing with carbon nanotube layers coated on silica fibers: Carrier transport versus nanoantenna effects

Carbon nanotube layers prepared as coatings on silica fibers are found to be suitable for terahertz detection in 0.5–7.3 THz range within temperatures of 4.2–70 K. In time-domain of terahertz excitation, two following constituents in the photoresponse are discriminated: the first one is attributed to the bolometric effect while the other one is related to the photoconductivity caused by the terahertz-induced hopping effect. In frequency domain, nonmonotonic behavior of the photoconductivity is associated with prevailing carbon nanotube-induced antenna effects in the electronic transport. The experimental observations are supported by theoretical estimates.

Scattering of Electromagnetic Waves by a Semi-Infinite Carbon Nanotube

Summary Scattering of electromagnetic cylindrical waves by an isolated, semi-infinite, open-ended, single-shell, zigzag carbon nanotube (CN) is considered in the optical regime. The CN is modeled as a smooth homogeneous cylindrical surface with impedance boundary conditions known from quantum-mechanical transport theory. An exact solution of the diffraction problem is obtained by the Wiener-Hopf technique. The differences between the scattering responses of metallic and semiconducting CNs are discussed.

Nanoscale Electromagnetic Compatibility: Quantum Coupling and Matching in Nanocircuits

The paper investigates two typical electromagnetic compatibility (EMC) problems, namely, coupling and matching in nanoscale circuits composed of nano-interconnects and quantum devices in entangled state. Nano-interconnects under consideration are implemented by using carbon nanotubes or metallic nanowires (NWs), while quantum devices by semiconductor quantum dots. Equivalent circuits of such nanocircuits contain additional elements arising at nanoscale due to quantum effects. As a result, the notions of coupling and impedance matching are reconsidered. Two examples are studied: in the first one, electromagnetically coupled NWs are connected to classical lumped devices; in the second one, electromagnetically uncoupled transmission lines are terminated on quantum devices in entangled states. In both circuits, the EMC features qualitatively and quantitatively differ from their classical analogs. In the second example, we demonstrate the existence of quantum coupling, due to the entanglement, which exists in spite of the absence of classical electromagnetic coupling. The entanglement also modifies the matching condition introducing a dependence of the optimal value of load impedance on the line length.

Scattering of the near field of an electric dipole by a single-wall carbon nanotube

The use of carbon nanotubes as optical probes for scanning near-field optical mi- croscopy requires an understanding of their near-field response. As a first step in this direction, we investigated the lateral resolution of a carbon nanotube tip with respect to an ideal electric dipole representing an elementary detected object. A Fredholm integral equation of the first kind was formulated for the surface electric current density induced on a single-wall carbon nanotube (SWNT) by the electromagnetic field due to an arbitrarily oriented electric dipole lo- cated outside the SWNT. The response of the SWNT to the near field of a source electric dipole can be classified into two types, because surface-wave propagation occurs with (i) low damp- ing at frequencies less than ∼ 200-250 THz and (ii) high damping at higher frequencies. The interaction between the source electric dipole and the SWNT depends critically on their rela- tive location and relative orientation, and shows evidence of the geometrical resonances of the SWNT in the low-frequency regime. These resonances disappear when the relaxation time of the SWNT is sufficiently low. The far-field radiation intensity is much higher when the source electric dipole is placed near an edge of SWNT than at the centroid of the SWNT. The use of an SWNT tip in scattering-type scanning near-field optical microscopy can deliver a resolution less than ∼ 20 nm. Moreover, our study shows that the relative orientation and distance between the SWNT and the nanoscale dipole source can be detected.

Electrodynamics of chiral carbon nanotubes in the helical parametrization scheme

Basic equations of electrodynamics of carbon nanotubes (CNTs are formulated in the helical parametrization scheme, where the crystalline structure of non-zigzag (n_1,n_2) CNTs is described as a set of n_2 double helices, and the electron energy spectrum of the CNTs consists of n_2 different helicoidal branches. The parametrization scheme is shown to be natural and more convenient for analyzing the electromagnetic response properties of chiral CNTs. Bloch equations for the density matrix have been obtained and adapted for the helical parametrization that allows studying the interaction between chiral CNTs and electromagnetic fields with arbitrary polarization and spatial structure. Linear transverse conductivity of chiral CNTs has been derived and utilized for the formulation of the effective boundary conditions for electromagnetic field on the surface of a chiral CNT. As an example, the spectra of high-order harmonics in chiral CNTs have been evaluated from the Bloch equations.

Array of tunneling-coupled quantum dots as a terahertz range quantum nanoantenna

Abstract. A terahertz range nanoantenna of a new type was conceptualized. The physical mechanism underlying the concept is population waveguiding, the Rabi wave, in tunneling-coupled one-dimensional and two-dimensional arrays of quantum dots (QDs) excited by the light wave traveling along the antenna. The terahertz component of the emission is stimulated by the tunneling current induced on the Rabi frequency by the motion of quantum transitions along the QD array. We calculated the antenna characteristics for the Rabi-wave loop nanoantenna and found its emission characteristics to be electrically tunable via varying the intensity and phase velocity of the light wave. The conceptualized antennas are promising for many practical applications due to their ability of electrical scanning of the antenna radiation pattern.