  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.
