Geometric Protection of Helical Edge States in Trivial Cylindrical Quantum Dots

Here we investigate electronic and transport properties of InAs_1-xBi_x quantum dots (QDs) in both topological and trivial regimes. We show through calculations that Bi-alloyed InAs quantum wells become 2D topological insulators with large inverted band gaps ~ 30 meV (> k_BT) for well widths larger than 7nm and x=0.15. By solving the proper BHZ model we find for cylindrical soft and hard walls confinement analytical expressions for the wave functions and circulating currents with energy levels determined from a transcendental equation. Interestingly, we find that trivial QDs have counter-propagating helical edge-like valence states that are shown to be "geometrically protected" over a wide range of QD radii. We calculate the circulating current densities for both topological and trivial edge states, where we find a higher density peak for trivial QDs while the integrated currents over half of QD cross section show no substantial difference. We have also calculated via Green's function the two-terminal linear conductance and find distinctive features between both regimes due to the energy degeneracy of the bulk and edge-like states in trivial QDs.