Tuning the vertical location of helical surface states in topological insulator heterostructures via dual-proximity effects

Abstract

In integrating topological insulators (TIs) with conventional materials, one crucial issue is how the topological surface states (TSS) will behave in such heterostructures. We use first-principles approaches to establish accurate tunability of the vertical location of the TSS via intriguing dual-proximity effects. By depositing a conventional insulator (CI) overlayer onto a TI substrate (Bi₂Se or Bi₂Te₃), we demonstrate that, the TSS can float to the top of the CI film, or stay put at the CI/TI interface, or be pushed down deeper into the otherwise structurally homogeneous TI substrate. These contrasting behaviors imply a rich variety of possible quantum phase transitions in the hybrid systems, dictated by key material-specific properties of the CI. These discoveries lay the foundation for accurate manipulation of the real space properties of TSS in TI heterostructures of diverse technological significance.

Figure 1. Schematic illustration on tuning the vertical location of the topological surface states (TSS) as a topological insulator (TI) is covered with a layer of conventional insulator (CI).

(a), TSS floating to the top of the CI. (b), Staying put at the CI/TI interface. (c), Diving into the TI. (d), The atomic structure of ZnM/Bi₂Se₃ (M = S, Se, Te). The red lines denote the TSS; the arrows indicate the resulting directions of the topological phase transition.

Figure 2. Band structures of ZnS/Bi₂Se₃ (upper row) and ZnSe/Bi₂Se₃ (lower row) along the K–Γ–M direction.

The dots indicate the electronic bands contributed by the CI (a) and (e), the 1^st QL of the TI (b) and (f), and the 6^th QL (c) and (g), respectively; the sizes and colors of the dots also indicate different spectral weights and contributions from different atoms, respectively. (d) and (h) show the charge density distribution of the upper-surface TSS at the Γ point marked by the circle and indicated by DP_U. The DP_U/L stands for the Dirac point at the upper/lower surface. The grey and cyan bars denote the locations of the different QLs and the CI, respectively.

Figure 3. Band structures of ZnTe/Bi₂Se₃ and ZnTe/Bi₂Se₃ along the K–Γ–M direction.

Band structures of the relaxed ZnTe/Bi₂Se₃ system (top row), the ZnTe/Bi₂Se₃ system with an increased separation of 3 Å from 2.5 Å between the 1^st QL and 2^nd QL of the TI substrate (second row), the ZnTe/Bi₂Se₃ system with an increased separation of 3 Å from 2.6 Å between the CI and 1^st QL (third row), and the relaxed ZnTe/Bi₂Se₃ system (bottom row). All other symbols are the same as in Fig. 2.

Figure 4. Illustrations on the effects of the key physical parameters on topological phase transitions.

(a), Weak interfacial coupling. (b & c), Moderate interfacial coupling, but with different spin-orbit coupling strengths. (d), Strong interfacial coupling. The red triangles denote the TSS; the solid and dotted black curves correspond to the valence bands of the CI and the Fermi level of the heterostructures, respectively.