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A topological insulator is a material whose interior behaves as an electrical insulator while its surface behaves as an electrical conductor, meaning that electrons can only move along the surface of the material. A topological insulator is an insulator for the same reason a "trivial" (ordinary) insulator is: there exists an energy gap between the valence and conduction bands of the material. But in a topological insulator, these bands are, in an informal sense, "twisted", relative to a trivial insulator.
Surface states are electronic states found at the surface of materials. They are formed due to the sharp transition from solid material that ends with a surface and are found only at the atom layers closest to the surface. The termination of a material with a surface leads to a change of the electronic band structure from the bulk material to the vacuum. In the weakened potential at the surface, new electronic states can be formed, so called surface states.
The topology of the electron wavefunctions in certain band insulators can give rise to novel topological phases. Materials harbouring such topological phases are termed topological insulators (TI). A
Binary bismuth chalcogenides Bi2Se3, Bi2Te3, and related materials are currently being extensively investigated as the reference topological insulators (TIs) due to their simple surface-state band dis