  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 (Bi2Se3 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.
