Suppressed Stark shift of helical edge states in topological-insulator quantum dots

Abstract

We study the stability of the electronic states in circular two-dimensional topological-insulator quantum dots against electric perturbations, as quantified by the susceptibility $\ensuremath{\chi}$ of the Stark shift $\mathrm{\ensuremath{\Delta}}E=\ensuremath{\chi}{F}^{2}/2$ of each energy level due to a small electric field $F$. We find the typical susceptibility ${\ensuremath{\chi}}_{\mathrm{edge}}\ensuremath{\sim}1$ meV/(mV/${\mathrm{nm})}^{2}$ for edge states is 4 orders of magnitude smaller than ${\ensuremath{\chi}}_{\mathrm{bulk}}\ensuremath{\sim}{10}^{4}$ meV/(mV/${\mathrm{nm})}^{2}$ for normal bulk states. We show that the origin of this strong stability of the edge states is the equidistance nature of the edge states, which follows from the linear dispersion of the one-dimensional edge channel. Therefore, we expect this strong stability to be a general feature for edge states in relatively large topological-insulator quantum dots. This finding identifies a new physical mechanism for protecting the edge states against electrical perturbations, which may be relevant to the applications of these edge states in quantum technologies.