Chirality effects in carbon nanotubes

Abstract

We consider chirality related effects in optical, photogalvanic and electron-transport properties of carbon nanotubes. We show that these properties of chiral nanotubes are determined by terms in the electron effective Hamiltonian describing the coupling between the electron wavevector along the tube principal axis and the orbital momentum around the tube circumference. We develop a theory of photogalvanic effects and a theory of d.c. electric current, which is linear in the magnetic field and quadratic in the bias voltage. Moreover, we present analytic estimations for the natural circular dichroism and magneto-spatial effect in the light absorption.Comment: 23 pages, 3 figure

Nonlinear coherent magneto-optical response of a single chiral carbon nanotube

“…An estimate for the circular dichroism of a (5, 4) nanotube can be calculated from [41], equation (44), giving a value of 1.03 for the relative difference between σ + and σ − absorption probability rates. This value, however, cannot be directly compared with the obtained result since the nanotube length does not enter the model in [41], and thus can only serve as a guide.…”

“…This value, however, cannot be directly compared with the obtained result since the nanotube length does not enter the model in [41], and thus can only serve as a guide. We should stress that our analysis applies to the high-intensity nonlinear ultrafast regime, in which, to the best of our knowledge, no theory or experiments have been published.…”

“…Owing to the combined effect of the AB and Zeeman energy levels shift, the dipole matrix element is modified. An estimate of the optical dipole matrix element in an axial magnetic field can be obtained from the theory developed in [41], taking into account the bandgap reduction at B = 8 T, giving ℘ = 3.6205 × 10 −29 Cm. Note that this value is slightly different from the zero magnetic field value (see appendix B).…”

“…In order to get an estimate of the dipole matrix element, we employ an extension of the effective mass method applied to chirality effects in CNTs proposed in [41]. It has been shown that chirality effects can be described by an effective Hamiltonian, in which the coupling between the electron wavevector k z along the tube axis and the quasiangular momentum around the tube circumference is taken into account.…”

“…Most importantly, the two approaches are similar in the following. Unlike other theories [28,41], both approaches do not consider the interference between the axial and helical paths (or equivalently, the axial and transverse wavevectors coupling) as the origin of the chirality effects. The spiral model provides a 1D periodic (zero field) electron dispersion law with periodic energy dependence on the electromagnetic field and predicts a uniform shift of the positions of the periodic minima in the dispersion when a magnetic field is applied.…”