Blurring the Boundaries Between Topological and Nontopological Phenomena in Dots.

We investigate the electronic and transport properties of topological and nontopological InAs_{0.85}Bi_{0.15} quantum dots (QDs) described by a ∼30  meV gapped Bernevig-Hughes-Zhang (BHZ) model with cylindrical confinement, i.e., "BHZ dots." Via modified Bessel functions, we analytically show that nontopological dots quite unexpectedly have discrete helical edge states, i.e., Kramers pairs with spin-angular-momentum locking similar to topological dots. These unusual nontopological edge states are geometrically protected due to confinement for a wide range of parameters and remarkably contrast with the bulk-edge correspondence in topological insulators, as no bulk topological invariant guarantees their existence. Moreover, for a conduction window with four edge states, we find that the two-terminal conductance G versus the QD radius R and the gate V_{g} controlling its levels shows a double peak at 2e^{2}/h for both topological and trivial BHZ QDs. This is in stark contrast to conductance measurements in 2D quantum spin Hall and trivial insulators. All of these results were also found in HgTe QDs. Bi-based BHZ dots should also prove important as hosts to room temperature edge spin qubits.