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

Abstract

We investigate the electronic and transport properties of topological and trivial InAs${}_{1-x}$Bi${}_x$ quantum dots (QDs). By considering the rapid band gap change within valence band anticrossing theory for InAs${}_{1-x}$Bi${}_x$, we predicted that Bi-alloyed quantum wells become $\sim 30$meV gapped 2D topological insulators for well widths $d>6.9$nm $(x=0.15)$ and obtain the $\mathbf{k}.\mathbf{p}$ parameters of the corresponding Bernevig-Hughes-Zhang (BHZ) model. We analytically solve this model for cylindrical confinement via modified Bessel functions. For non-topological dots we find "geometrically protected" discrete helical edge-like states, i.e., Kramers pairs with spin-angular-momentum locking, in stark contrast with ordinary InAs QDs. For a conduction window with four edge states, we find that the two-terminal conductance $\mathcal{G}$ vs. 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 QDs. In contrast, when bulk and edge-state Kramers pairs coexist and are degenerate, a single-peak resonance emerges. Our results blur the boundaries between topological and non-topological phenomena for conductance measurements in small systems such as QDs. Bi-based BHZ QDs should also prove important as hosts to edge spin qubits.

Main text (4 pages + 3 figures) and Supplemental Material