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Confined electronic states and optical transitions in 3D topologicalinsulator nanoparticles have been studied in the literature, assuming idealizedgeometries such as spheres or infinitely long cylinders, that allow to obtainanalytical solutions to the corresponding eigenvalue equation within suchgeometries. In contrast, in this article we consider triangular-shapednanoplates as a more realistic approximation to the experimentally observedmorphologies of topological insulator nanoparticles. In this particulargeometry, we obtain analytical expressions for the confined eigenstates and thecorresponding energy spectrum. Moreover, by a spatial representation of theprobability density distribution of these states, we further identify theconditions leading to the emergence of topologically trivial surface states asa result of geometric confinement. Finally, we also study the opticaltransitions and the corresponding selection rules imposed by the nanoparticlesize and morphology.

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