Blurring the boundaries between topological and non-topological phenomena in dots

In this work we investigate the electronic and transport properties of topological and non-topological InAs_0.85Bi_0.15 quantum dots (QDs) described by a Bernevig-Hughes-Zhang (BHZ) model with cylindrical confinement, i.e., "BHZ dots''. We analytically show that {\it non-topological} dots have discrete helical edge states, i.e., Kramers pairs with spin-angular-momentum locking similar to topological dots. These unusual and unexpectedly non-topological edge states are geometrically protected due to confinement in a wide range of parameters and are not guaranteed to exist by the bulk-edge correspondence. In addition, for a conduction window with four edge states, we find that the two-terminal conductance G vs. the QD radius R and the gate V_g controlling its levels shows a double peak at 2e²/h for both topological and trivial BHZ QDs. Our results blur the boundaries between topological and non-topological phenomena for conductance measurements in small systems such as QDs thus showing an equivalence between the BHZ QDs in different topological phases.