Electronic properties of one-dimensional nanostructures of the Bi$_2$Se$_3$ topological insulator

TL;DR

This paper provides a theoretical analysis of the electronic and spin properties of one-dimensional Bi$_2$Se$_3$ nanostructures, revealing how confinement and geometry influence their topological surface states and potential spintronics applications.

Contribution

It introduces realistic models of Bi$_2$Se$_3$ nanowires and nanoribbons, analyzing their band structures and spin textures considering circumferential confinement effects.

Findings

Band structures consist of evenly spaced degenerate sub-bands.

Band gaps depend on the nanostructure circumference.

Surface spin density oscillates with charge-carrier energy.

Abstract

We theoretically study the electronic structure and spin properties of one-dimensional nanostructures of the prototypical bulk topological insulator Bi$_2$Se$_3$. Realistic models of experimentally observed Bi$_2$Se$_3$ nanowires and nanoribbons are considered using the tight-binding method. At low energies, the band structures are composed of a series of evenly spaced degenerate sub-bands resulting from circumferential confinement of the topological surface states. The direct band gaps due to the non-trivial $\pi$ Berry phase show a clear dependence on the circumference. The spin-momentum locking of the topological surface states results in a pronounced 2$\pi$ spin rotation around the circumference with the degree of spin polarization dependent on the the momentum along the nanostructure. Overall, the band structures and spin textures are more complicated for nanoribbons, which expose two distinct facets. The effects of reduced dimensionality are rationalized with the help of a simple model that considers circumferential quantization of the topological surface states. Furthermore, the surface spin density induced by electric current along the nanostructure shows a pronounced oscillatory dependence on the charge-carrier energy, which can be exploited in spintronics applications.