Effective Hamiltonian for surface states of topological insulator nanotubes

TL;DR

This paper derives an effective Hamiltonian for the surface states of topological insulator nanotubes, accounting for curvature and dual surfaces, and analyzes how these factors influence electronic properties.

Contribution

It introduces a novel effective Hamiltonian for TI nanotubes that includes curvature effects and inner-outer surface coupling, extending prior flat film models.

Findings

Parameters vary with nanotube dimensions

Eigenstate behavior differs with tube size

Curvature induces unique spin-orbit effects

Abstract

In this work we derive an effective Hamiltonian for the surface states of a hollow topological insulator (TI) nanotube with finite width walls. Unlike a solid TI cylinder, a TI nanotube possesses both an inner as well as outer surface on which the states localized at each surface are coupled together. The curvature along the circumference of the nanotube leads to a spatial variation of the spin orbit interaction field experienced by the charge carriers as well as an asymmetry between the inner and outer surfaces of the nanotube. Both of these features result in terms in the effective Hamiltonian for a TI nanotube absent in that of a flat TI thin film of the same thickness. We calculate the numerical values of the parameters for a \ce{Bi2Se3} nanotube as a function of the inner and outer radius, and show that the differing relative magnitudes between the parameters result in qualitatively differing behaviour for the eigenstates of tubes of different dimensions.