Design Principles and Coupling Mechanisms in the 2D Quantum-Well Topological Insulator HgTe/CdTe

We present atomistic band structure calculations revealing a different mechanism than recently surmised via {$\bf k\cdot p$} calculations about the evolution of the topological state (TS) in HgTe/CdTe. We show that {\it 2D interface} (not {\it 1D edge}) TS are possible. We find that the transitions from a topological insulator at critical HgTe thickness of $n= 23$ ML (62.5 {\AA}) to a normal insulator at smaller $n$ is due to the crossing between two interface localized states: one derived from the S-like $\Gamma_{6c}$ and one derived from the P-like $\Gamma_{8v}$ light-hole, not because of the crossing of an interface state and an extended QW state. These atomistic calculations suggest that a 2D TS can exist in a 2D system, even without truncating its symmetry to 1D, thus explaining the otherwise surprising similarity between the 2D dispersion curves of the TS in HgTe/CdTe with those of the TS in 3D bulk materials such as Bi$_2$Se$_3$. Ref: J.W. Luo and A. Zunger, Phys. Rev. Lett. {\bf 105}, 176805 (2010).