Band structure of nanotubes with spin-orbit interaction

What is it about?

In recent years, silicene, germanene, and stanene have received considerable attention due to their potential to exhibit a spin Hall effect. Nanoribbons made of these materials are expected to have topologically protected states. In this work, we study the electronic properties of nanotubes made of Si, Ge, Sn, and functionalized Sn. The main difference between these materials and graphene is the significance of spin-orbit interaction. 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 band gap of a nanotube by applying an external radial electric field.

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Why is it important?

In this study, we propose a device in which an external electric field is applied perpendicularly to the surface of the cylinder. By applying this external field, the band gap can be controlled. At a critical field the gap closes, and the NTs transition from a trivial insulating band to a metallic system. We found that in some cases, with this field, electrons with different spins move in opposite directions. By controlling the electric field using a gate potential, this device can function as a field-effect transistor, where the conductance can be modified with the gate.