Signatures of spin-orbit interaction in transport properties of finite carbon nanotubes in a parallel magnetic field

Abstract

The transport properties of finite nanotubes placed in a magnetic field parallel to their axes are investigated. Upon including spin-orbit coupling and curvature effects, two main phenomena are analyzed that crucially depend on the tube's chirality: (i) Finite carbon nanotubes in a parallel magnetic field may present a suppression of current due to the localization at the edges of otherwise conducting states. This phenomenon occurs due to the magnetic-field-dependent open boundary conditions obeyed by the carbon nanotube's wave functions. The transport is fully suppressed above threshold values of the magnetic field, which depend on the nanotube chirality, length, and on the spin-orbit coupling. (ii) Reversible spin-polarized currents can be obtained upon tuning the magnetic field, exploiting the curvature-induced spin-orbit splitting.

The two classes of low-energy spectra in finite carbon nanotubes

“…The SOI breaks both the U symmetry and the degeneracy between the states | k,σ and |− k,σ [22]. The time-reversal and C n symmetries are preserved and the spectrum consists of a series of Kramers' doublets.…”

“…This relation, shown here in the translational scheme in which it usually is derived, is the standard momentum quantization condition for pure zigzag CNTs [22,27].…”

“…We have performed this diagonalization, including the curvature effects [21,22], with the hopping integrals between π and σ orbitals set to V π = −2.66 and V σ = 6.38 eV [26]. In the following, we present our analytical derivation of the spectra together with the numerical results.…”

“…For simplicity, the spin degree of freedom and spin-orbit interaction effects will be discussed later. The hopping integrals t R, R+ d depend on the CNT's curvature [21,22]. In infinite CNTs, we can define the sublattice states…”

“…Figs. 2(a) and 2(c)] [21,22]. The Dirac momenta ± K c correspond in the helical representation to (±m, ± K c ), with m = 0 in CNTs of the (Z) class.…”