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

## TL;DR

This study explores the electronic properties of InAsBi quantum dots, revealing that both topological and trivial dots exhibit similar conductance features, blurring the distinction between topological and non-topological phenomena.

## Contribution

It introduces a detailed analysis of InAsBi quantum dots, demonstrating the coexistence of topological and trivial edge states and their impact on conductance, expanding understanding of quantum dot topological properties.

## Key findings

- Both topological and trivial QDs show conductance peaks at 2e^2/h.
- Geometrically protected edge-like states exist in trivial QDs.
- Conductance features can be similar for topological and non-topological 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 $\boldsymbol{k.p}$ 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 ${\cal G}$ 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.