Tsuneya Ando

Theory of Electronic States and Transport in Carbon Nanotubes

A brief review is given of electronic and transport properties of carbon nanotubes obtained mainly in a k · p scheme. The topics include a giant Aharonov–Bohm effect on the band gap and a Landau-level formation in magnetic fields, magnetic properties, interaction effects on the band structure, optical absorption spectra, and exciton effects. Transport properties are also discussed including absence of backward scattering except for scatterers with a potential range smaller than the lattice constant, its extension to multi-channel cases, a conductance quantization in the presence of short-range and strong scatterers such as lattice vacancies, and transport across junctions between nanotubes with different diameters. A continuum model for phonons in the long-wavelength limit and the resistivity determined by phonon scattering are reviewed as well.

Electronic States of Carbon Nanotubes

The π-electron states of carbon nanotubes (CNs) in magnetic fields are calculated in the effective-mass theory. A sensitive change of CN from metal to semiconductor depending on its structure is well reproduced. The band gap is inversely proportional to the tube diameter and exhibits a drastic change as a function of magnetic flux passing through the cylinder with period c h / e due to the Aharonov-Bohm effect. In a magnetic field perpendicular to the tube axis, the band-gap is reduced strongly and the energy spectra approach those of a graphite sheet.

Excitons in Carbon Nanotubes

Exciton energy levels and corresponding optical spectra are calculated in carbon nanotubes (CN) in the conventional screened Hartree-Fock approximation within a k · p scheme. The Coulomb interaction gives rise to several exciton bound states as well as the increase of the energy gap. The exciton energy is shifted to higher energy side than the unperturbed band gap because the effect on the band gap is larger. The considerable amount of the optical intensity is transferred to exciton bound states because of the one-dimensional nature of CNs.

Theory of Quantum Transport in a Two-Dimensional Electron System under Magnetic Fields. I. Characteristics of Level Broadening and Transport under Strong Fields

Characteristics of level broadening and transverse conductivity of a two-dimensional electron system under extremely strong fields have been theoretically investigated in the simplest approximation without the difficulty of divergence, i e. in the so-called damping theoretical one. Those of various cases of short- and long-ranged scatterers have been obtained. To see the dependence on the range explicitly, numerical calculation has been performed for the system with scatterers with the Gaussian potential. Especially in case of short-ranged ones the peak value of the transverse conductivity has been shown to be \((N+1/2)e^{2}/\pi^{2}\hbar\) which depends only on the natural constants and the Landau level index. It has been argued from general point of view that this fact is approximately true without reference to kinds of approximations. Such characteristic of the conductivity was confirmed experimentally, but there still remain some problems as to the absolute value of the level width.

Screening Effect and Impurity Scattering in Monolayer Graphene

The static polarization function is calculated in two-dimensional graphite and used for the calculation of the conductivity limited by charged-impurity scattering. The conductivity increases in proportion to the electron concentration and the mobility remains independent of the Fermi energy, in qualitative agreement with experiments. The screening increases in proportion to temperature at sufficiently high temperatures in contrast to the behavior in conventional two-dimensional systems, leading to the mobility increase proportional to the square of temperature.

Berry's Phase and Absence of Back Scattering in Carbon Nanotubes

The absence of back scattering in carbon nanotubes is shown to be ascribed to Berrys phase which corresponds to a sign change of the wave function under a spin rotation of a neutrino-like particle in a two-dimensional graphite. Effects of trigonal warping of the bands appearing in a higher order k · p approximation are shown to give rise to a small probability of back scattering.

Aharonov-Bohm effect in carbon nanotubes

Abstract Optical absorption spectra are calculated in carbon nanotubes in the presence of a magnetic flux parallel to the tube axis. A drastic change in the band gap manifests itself in optical spectra for light polarization parallel to the axis. In the case of perpendicular polarization, the absorption is suppressed by a large depolarization effect.

Impurity Scattering in Carbon Nanotubes – Absence of Back Scattering –

The effective potential of an impurity in a k · p scheme is derived in two-dimensional graphite sheet. When the potential range is smaller than the lattice constant, it has an off-diagonal matrix element between K and K ′ points comparable to the diagonal element. With the increase of the range, this off-diagonal element decreases rapidly and the diagonal element for envelopes at A and B sites becomes identical. The crossover between these two regimes occurs around the range smaller than the lattice constant. In the latter regime, back scattering between states with + k and - k vanishes identically for the bands crossing the Fermi level in the absence of a magnetic field, leading to an extremely large conductivity. The absence of the back scattering disappears in magnetic fields, giving rise to a huge positive magnetoresistance.

Quantum Transport in Two-Dimensional Graphite System

In a self-consistent Born approximation, the density of states and the conductivity are calculated in a two-dimensional graphite sheet in magnetic fields. Two different cases of scatterers are considered, the short-range case where the range is smaller than the lattice constant and the long-range case where it is comparable or slightly larger. The quantum theory provides results quite different from the results of Boltzmann transport theory even in the absence of a magnetic field. In high magnetic fields, the conductivity exhibits a series of peaks, whose values depend only on the natural constants and the Landau level index. The conductivity of undoped systems is always given by a universal conductivity \(e^{2}/\pi^{2}\hbar\) independent of a magnetic field.

Self-Consistent Results for a GaAs/AlxGa1-xAs Heterojunciton. II. Low Temperature Mobility

The low temperature mobility is calculated in a two-dimensional system at a GaAs/Al x Ga 1- x As heterojunction. Scattering mechanisms are assumed to be the Coulomb scattering from ionized donors in the Al x Ga 1- x As layer, interface roughness, and scattering caused by alloy disorder present in the Al x Ga 1- x As layer. The calculated mobility for the Coulomb scattering explains recent experimental results. The interface roughness and the alloy scattering can play a role at high electron concentrations (∼10 12 cm -2 ).