Topological insulator

A topological insulator is a material with non-trivial symmetry-protected 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. However, having a conducting surface is not unique to topological insulators, since ordinary band insulators can also support conductive surface states. What is special about topological insulators is that their surface states are symmetry-protected by particle number conservation and time-reversal symmetry. A topological insulator is a material with non-trivial symmetry-protected 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. However, having a conducting surface is not unique to topological insulators, since ordinary band insulators can also support conductive surface states. What is special about topological insulators is that their surface states are symmetry-protected by particle number conservation and time-reversal symmetry. 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. On the surface of a topological insulator there are special states that fall within the bulk energy gap and allow surface metallic conduction. Carriers in these surface states have their spin locked at a right-angle to their momentum (spin-momentum locking). 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. Non-interacting topological insulators are characterized by an index (known as Z 2 {displaystyle mathbb {Z} _{2}} topological invariants) similar to the genus in topology. As long as time-reversal symmetry is preserved (i.e., there is no magnetism), the Z 2 {displaystyle mathbb {Z} _{2}} index cannot change by small perturbations and the conducting states at the surface are symmetry-protected. On the other hand, in the presence of magnetic impurities, the surface states will generically become insulating. Nevertheless, if certain crystalline symmetries like inversion are present, the Z 2 {displaystyle mathbb {Z} _{2}} index is still well defined. These materials are known as magnetic topological insulators and their insulating surfaces exhibit a half-quantized surface anomalous Hall conductivity. Time-reversal symmetry-protected two-dimensional edge states were predicted in 1987 by Oleg Pankratov to occur in quantum wells (very thin layers) of mercury telluride sandwiched between cadmium telluride, and were observed in 2007. In 2006, it was predicted that similar topological insulators might be found in binary compounds involving bismuth, and in particular 'strong topological insulators' exist that cannot be reduced to multiple copies of the quantum spin Hall state. The first experimentally-realized 3D topological insulator state (symmetry-protected surface states) was discovered in bismuth-antimony in 2008. Shortly thereafter symmetry-protected surface states were also observed in pure antimony, bismuth selenide, bismuth telluride and antimony telluride using angle-resolved photoemission spectroscopy (ARPES). Many semiconductors within the large family of Heusler materials are now believed to exhibit topological surface states. In some of these materials, the Fermi level actually falls in either the conduction or valence bands due to naturally-occurring defects, and must be pushed into the bulk gap by doping or gating. In 2012, topological Kondo insulators were discovered in samarium hexaboride, which is a bulk insulator at low temperatures. The surface states of a 3D topological insulator is a new type of two-dimensional electron gas (2DEG) where the electron's spin is locked to its linear momentum. Fully bulk-insulating or intrinsic 3D topological insulator states exist in Bi-based materials. In 2014, it was shown that magnetic components, like the ones in spin-torque computer memory, can be manipulated by topological insulators. The effect is related to metal–insulator transitions (Bose–Hubbard model).