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In integrating topological insulators (TIs) with conventional materials, onecrucial issue is how the topological surface states (TSS) will behave in suchheterostructures. We use first-principles approaches to establish accuratetunability of the vertical location of the TSS via intriguing dual-proximityeffects. By depositing a conventional insulator (CI) overlayer onto a TIsubstrate (Bi2Se3 or Bi2Te3), we demonstrate that, the TSS can float to the topof the CI film, or stay put at the CI/TI interface, or be pushed down deeperinto the otherwise structurally homogeneous TI substrate. These contrastingbehaviors imply a rich variety of possible quantum phase transitions in thehybrid systems, dictated by key material-specific properties of the CI. Thesediscoveries lay the foundation for accurate manipulation of the real spaceproperties of TSS in TI heterostructures of diverse technological significance.

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