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evidence: A topological insulator is a material with non-trivial topological order that behaves as an insulator in its interior but whose surface contains conducting states , meaning that electrons can only move along the surface of the material .. topological order. topological order. insulator. Insulator ( electrical ). conducting. Electrical conductivity. However , the conducting surface is not the unique character of topological insulators , since the ordinary band insulators can also support conductive surface states .. conducting. Electrical conductivity. What is special is that the surface states of topological insulators are symmetry protected by particle number conservation and time reversal symmetry .. symmetry protected. Symmetry protected topological order. In the bulk of a non-interacting topological insulator , the electronic band structure resembles an ordinary band insulator , with the Fermi level falling between the conduction and valence bands .. insulator. Insulator ( electrical ). electronic band structure. electronic band structure. Fermi level. Fermi level. On the surface of a topological insulator there are special states that fall within the bulk energy gap and allow surface metallic conduction .. insulator. Insulator ( electrical ). Carriers in these surface states have their spin locked at a right-angle to their momentum -LRB- spin-momentum locking -RRB- .. spin. Spin quantum number. At a given energy the only other available electronic states have different spin , so the `` U '' - turn scattering is strongly suppressed and conduction on the surface is highly metallic .. spin. Spin quantum number. Non-interacting topological insulators are characterized by an index -LRB- known as Z2 topological invariants -RRB- similar to the genus in topology .. genus. Genus ( mathematics ). The `` protected '' conducting states in the surface are required by time-reversal symmetry and the band structure of the material .. conducting. Electrical conductivity. time-reversal symmetry. time-reversal symmetry. The states can not be removed by surface passivation if it does not break the time-reversal symmetry , which does not happen with potential and / or spin-orbit scattering , but happens in case of true magnetic impurities -LRB- e.g. spin-scattering -RRB- .. spin. Spin quantum number. time-reversal symmetry. time-reversal symmetry. surface passivation. Passivation ( chemistry )