Hiroshi Ajiki

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.

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.

Magnetic properties of carbon nanotubes

Magnetic properties of carbon nanotubes (CNs) are calculated in the effective-mass theory. The magnetic moment in a magnetic flux parallel to the tube axis oscillates as a function of the flux with period determined by the flux quantum and phase depending on whether CN is metallic or semiconducting. For a magnetic field perpendicular to the axis, CNs exhibit a large diamagnetism independent of metallic or semiconducting. The magnetic moment induced by a perpendicular field is about three order of magnitude as large as that by a parallel field.

Energy Bands of Carbon Nanotubes in Magnetic Fields

Electronic states of carbon nanotubes in a magnetic field perpendicular to the axis are studied in a tight-binding model and the validity of k · p theory is examined. The energy bands near the Fermi level calculated in the tight-binding model agree with those of k · p in a wide magnetic-field range except in extremely high fields where the flux passing through the unit cell of a two-dimensional graphite is comparable to the flux quantum, i.e. up to ∼4000 T. A slight deviation from the k · p result in weak magnetic fields can be explained by the inclusion of higher order terms in the k · p expansion leading to trigonal warping of bands.

Magnetic Properties of Ensembles of Carbon Nanotubes

Magnetic properties of carbon nanotubes (CNs) are studied in a k · p model. In a magnetic field perpendicular to the tube axis, the magnetization is essentially determined by that of a graphite sheet, while it is induced also by the Aharonov-Bohm (AB) effect in a parallel field. The AB effect manifests itself in the magnetic-field and temperature dependence of the differential susceptibility even for ensembles of CNs having various circumferences and orientations. The magnetic properties depend also on carrier doping.

Lattice instability in metallic carbon nanotubes

A lattice instability toward in-plane Kekule and out-of-plane distortions is studied in metallic carbon nanotubes in both k · p approximation and tight-binding model. The k · p model Hamiltonian is given by Diracs relativistic equation in the presence of distortion. The resulting gap equation is solved analytically in the presence of an Aharonov-Bohm magnetic flux through the cross section of nanotube, leading to the conclusion that the in-plane and out-of-plane distortions cannot coexist. A tight-binding model gives results in excellent agreement with k · p results and justifies the k · p model Hamiltonian.

Carbon Nanotubes: Optical Absorption in Aharonov-Bohm Flux

Optical absorption spectra for carbon nanotubes are calculated in the presence of an Aharonov-Bohm flux passing through the cross section. The band gap drastically changes with a period of the magnetic flux quantum because of the Aharonov-Bohm effect. The effect can be seen as a shift of the absorption peaks for light polarization parallel to the tube axis. For perpendicular polarization the absorption is strongly suppressed due to a depolarization effect.

Lattice Distortion of Metallic Carbon Nanotubes Induced by Magnetic Fields

A lattice instability toward in-plane Kekule and out-of-plane distortions is studied for metallic carbon nanotubes in a magnetic field perpendicular to the tube axis using a k · p approximation. A strong magnetic field drastically enhances the distortion for the nanotubes with larger circumference and leads to a gap almost independent of an Aharonov-Bohm magnetic flux passing through the cross section. For the Kekule distortion, in particular, the gap increases with the circumference length and approaches a value smaller than that of a 2D graphite sheet by a factor of 2/π

Lattice Distortion with Spatial Variation of Carbon Nanotubes in Magnetic Fields

A lattice instability of carbon nanotubes induced by a magnetic field perpendicular to the tube axis is studied in a k · p scheme. Both in-plane Kekule and out-of-plane distortions are enhanced drastically with increase of a magnetic field independent of whether a nanotube is metallic or semiconducting and magnetic flux passing through the cross section of a nanotube. The distortions become dependent on the position in the circumference direction.

Aharonov—Bohm effect on magnetic properties of carbon nanotubes

Abstract Magnetic properties of carbon nanotubes are studied in the context of the k·p model. They vary strongly as a function of carrier doping and strength of the applied magnetic field. The magnetization of ensembles of carbon nanotubes with different orientations and diameters is also calculated.