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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. [4]
The topological insulators and superconductors are classified here in ten symmetry classes (A,AII,AI,BDI,D,DIII,AII,CII,C,CI) named after Altland–Zirnbauer classification, defined here by the properties of the system with respect to three operators: the time-reversal operator , charge conjugation and chiral symmetry . The symmetry classes are ...
Magnetic topological insulators have proven difficult to create experimentally. In 2023 it was estimated that a magnetic topological insulator might be developed in 15 years' time. [16] A compound made from manganese, bismuth, and tellurium (MnBi2Te4) has been predicted to be a magnetic topological insulator.
Photonic topological phases are classical electromagnetic wave analogues of electronic topological phases studied in condensed matter physics. Similar to their electronic counterparts, they, can provide robust unidirectional channels for light propagation. [2] The field that studies these phases of light is referred to as topological photonics.
Topological insulators only have short-ranged entanglements and have no topological order, while the topological order defined in this article is a pattern of long-range entanglement. Topological order is robust against any perturbations.
Mercury telluride was the first topological insulator discovered, in 2007. Topological insulators cannot support an electric current in the bulk, but electronic states confined to the surface can serve as charge carriers .
Compatibility with a material's symmetries, as described by the magnetic space group, is a necessary condition for a variety of material properties, including ferromagnetism, ferroelectricity, topological insulation.
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...