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

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: $\mathit{\text{(i)}}$ 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 $\mathit{\text{(ii)}}$ 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.