Aharonov–Bohm Effect and Symmetry Crossover in Carbon Nanotubes

Tsuneya Ando

doi:10.1143/jpsj.75.054701

Abstract

Localization effects in a metallic carbon nanotube are studied as a function of Aharonov–Bohm magnetic flux. The conductance exhibits the behavior of strong localization except in the absence of a flux. When the Fermi level lies in higher bands, the localization effect becomes smaller at a half flux quantum due to the recovery of the time reversal symmetry. A clear symmetry crossover occurs due to perturbations such as trigonal band-warping and scatterers with potential range smaller than the lattice constant of the two-dimensional graphite.

Highlights

IntroductionBohm (AB) effect on the band structure.9,10) Recently, splitting of optical absorption and emission peaks due to flux was observed.11–13) In the presence of a magnetic flux the time-reversal symmetry is absent and the perfectly conducting channel is destroyed
In particular, the backward scattering is entirely suppressed for scatterers with potential range larger than the lattice constant of a two-dimensional graphite and the conductance is quantized into 2e2 =h .1,2) This has been related to Berry’s phase and associated topological anomaly present in Weyl’s equation describing the electron motion in two-dimensional graphite.3) When there are several bands coexist at the Fermi level, interband scattering appears but a perfectly transmitting channel is present and the conductance remains larger than 2e2 =h .4) The purpose of this paper is to study oscillation in localization effects as a function of magnetic flux passing through the cross section and to demonstrate symmetry crossover due to various perturbations
Potential range smaller than the lattice constant, no backward scattering is present and the conductance becomes ideal when the Fermi level lies in linear bands in metallic carbon nanotubes

Summary

Introduction

Bohm (AB) effect on the band structure.9,10) Recently, splitting of optical absorption and emission peaks due to flux was observed.11–13) In the presence of a magnetic flux the time-reversal symmetry is absent and the perfectly conducting channel is destroyed. When the flux is equal to a half of the flux quantum, the time-reversal symmetry is recovered but the channel number becomes even. In this case, the determinant of an antisymmetric matrix needs not vanish and the perfect channel is destroyed completely. The flux dependence in nanotubes is quite different from a 0 =2 oscillation of the conductance in metallic systems on a cylinder surface, first predicted theoretically15) and observed experimentally.16) This so-called AAS oscillation arises due to the symmetry change caused by the flux with period 0 =2

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Conclusion