The role of morphology on the emergence of topologically trivial surface states and selection rules in topological-insulator nano-particles

TL;DR

This paper investigates how the shape and size of topological insulator nanoparticles, especially triangular nanoplates, influence the emergence of trivial surface states and optical transition rules, providing analytical insights into realistic geometries.

Contribution

It introduces analytical solutions for eigenstates in triangular topological insulator nanoplates and links geometry to the emergence of trivial surface states and optical selection rules.

Findings

Analytical eigenstates for triangular nanoplate geometries.

Conditions for topologically trivial surface states due to confinement.

Impact of nanoparticle size and shape on optical transition rules.

Abstract

Confined electronic states and optical transitions in 3D topological insulator nanoparticles have been studied in the literature, assuming idealized geometries such as spheres or infinitely long cylinders, that allow to obtain analytical solutions to the corresponding eigenvalue equation within such geometries. In contrast, in this article we consider triangular-shaped nanoplates as a more realistic approximation to the experimentally observed morphologies of topological insulator nanoparticles. In this particular geometry, we obtain analytical expressions for the confined eigenstates and the corresponding energy spectrum. Moreover, by a spatial representation of the probability density distribution of these states, we further identify the conditions leading to the emergence of topologically trivial surface states as a result of geometric confinement. Finally, we also study the optical transitions and the corresponding selection rules imposed by the nanoparticle size and morphology.