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A topological insulator is a material with ''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. However, the conducting surface is not the unique character of topological insulator, since the ordinary band insulators can also support conductive surface states. What is special is that the surface states of topological insulators are symmetry protected〔 Zheng-Cheng Gu and Xiao-Gang Wen (Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order ) Phys. Rev. B80, 155131 (2009). 〕〔 〕〔Xie Chen, Zheng-Cheng Gu, Xiao-Gang Wen, (Classification of Gapped Symmetric Phases in 1D Spin Systems ) Phys. Rev. B 83, 035107 (2011); Xie Chen, Zheng-Xin Liu, Xiao-Gang Wen, (2D symmetry protected topological orders and their protected gapless edge excitations ) Phys. Rev. B 84, 235141 (2011)〕 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 Z2 topological invariants) similar to the genus in topology.〔 The "protected" conducting states in the surface are required by time-reversal symmetry and the band structure of the material. The states cannot 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 (e.g. spin-cattering).〔Th. Guhr, A. Müller-Groening, H.A. Weidenmüller: (''Random Matrix Theories in Quantum Physics: Common Concepts.'' ) In: ''Physics Reports'', volume 299, 1998, p. 189–425.〕 ==Prediction and discovery== Time-reversal symmetry protected edge states were predicted in 1987 to occur in quantum wells (very thin layers) of mercury telluride sandwiched between cadmium telluride and were observed in 2007. In 2007, they were predicted〔 〕 to occur in three-dimensional bulk solids of binary compounds involving bismuth. A 3D "strong topological insulator" exists which 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 antimonide. Shortly thereafter symmetry protected surface states were also observed in pure antimony, bismuth selenide, bismuth telluride and antimony telluride using 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. The surface states of a 3D topological insulator is a new type of 2DEG (two-dimensional electron gas) 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 (Nature Physics 2014) In 2012 several groups released preprints which suggest that samarium hexaboride has the properties of a topological insulator〔(【引用サイトリンク】publisher=Nature )〕 in accordance with the earlier theoretical predictions. Since samarium hexaboride is an established Kondo insulator, i.e. a strongly correlated electron material, the existence of a topological surface state in this material would lead to a topological insulator with strong electronic correlations. Stanene is a theoretical topological insulator which may display superconductivity at its edges above room temperature. A study published in July 2014 of Nature magazine demonstrates that magnetic components, like the ones in computer memory, can be manipulated by topological insulators.〔http://www.nature.com/nature/journal/v511/n7510/full/nature13534.html〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「topological insulator」の詳細全文を読む スポンサード リンク
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