Anomalous Finite Size Effects on Surface States in the Topological Insulator Bi$_2$Se$_3$

TL;DR

This study investigates how finite size affects surface states in the topological insulator Bi$_2$Se$_3$, revealing robustness of surface states and oscillating hybridization gaps, with implications for nanoscale quantum devices.

Contribution

It demonstrates the robustness of Bi$_2$Se$_3$ surface states against size reduction and identifies an oscillating decay in hybridization gaps, contrasting with previous findings in HgTe.

Findings

Surface states in Bi$_2$Se$_3$ remain intact down to a few nm width.

Hybridization gap exhibits oscillating exponential decay with size.

Bi$_2$Se$_3$ is promising for nanoscale quantum applications.

Abstract

We study how the surface states in the strong topological insulator Bi$_2$Se$_3$ are influenced by finite size effects, and compare our results with those recently obtained for 2D topological insulator HgTe. We demonstrate two important distinctions: \textit{(i)} contrary to HgTe, the surface-states in Bi$_2$Se$_3$ display a remarkable robustness towards decreasing the width $L$ down to a few nm, thus ensuring that the topological surface states remain intact, and \textit{(ii)} the gapping due to the hybridization of the surface states features an oscillating exponential decay as a function of $L$ in Bi$_2$Se$_3$ in sharp contrast to HgTe. Our findings suggest that Bi$_2$Se$_3$ is suitable for nanoscale applications in quantum computing or spintronics. Also, we propose a way to experimentally detect both of the predicted effects.