Effect of the spin–orbit interaction in nanotubes

Abstract

In this work, we study the electronic properties of nanotubes with spin–orbit interaction that exhibit a spin Hall effect. Nanoribbons made of these materials are expected to have topologically protected states. The lack of edge states in a seamless tube eliminates the possibility of finding a topological edge state. The spin–orbit interaction breaks the degeneracy of Dirac’s cones and eliminates the chance of finding a metal nanotube. As a consequence, this makes all nanotubes with spin–orbit interaction trivial band insulators. We focus our attention on two features. First, we study the energy band gap as a function of the diameter of the nanotubes. Then, we concentrate on controlling the bandgap of a nanotube by applying an external radial electric field. Finally, we discuss the possibility of using one of these tubes as a field-effect transistor.