Curvature-enhanced spin-orbit coupling in a carbon nanotube

TL;DR

This paper theoretically demonstrates that curvature in carbon nanotubes introduces two types of spin-orbit coupling, including a previously unrecognized diagonal contribution, affecting spintronic properties and energy level behaviors.

Contribution

The study reveals a new diagonal spin-orbit coupling term induced by curvature in carbon nanotubes, expanding understanding of spin-orbit interactions in curved graphene structures.

Findings

Curvature induces two types of spin-orbit coupling in carbon nanotubes.

The diagonal spin-orbit term can cause electron-hole asymmetric spin splitting.

Different behaviors of energy levels under magnetic fields are explained by the new term.

Abstract

Structure of the spin-orbit coupling varies from material to material and thus finding the correct spin-orbit coupling structure is an important step towards advanced spintronic applications. We show theoretically that the curvature in a carbon nanotube generates two types of the spin-orbit coupling, one of which was not recognized before. In addition to the topological phase-related contribution of the spin-orbit coupling, which appears in the off-diagonal part of the effective Dirac Hamiltonian of carbon nanotubes, there is another contribution that appears in the diagonal part. The existence of the diagonal term can modify spin-orbit coupling effects qualitatively, an example of which is the electron-hole asymmetric spin splitting observed recently, and generate four qualitatively different behavior of energy level dependence on parallel magnetic field. It is demonstrated that the diagonal term applies to a curved graphene as well. This result should be valuable for spintronic applications of graphitic materials.