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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 ...
Typical examples include graphene, topological insulators, bismuth antimony thin films and some other novel nanomaterials, [1] [4] [5] in which the electronic energy and momentum have a linear dispersion relation such that the electronic band structure near the Fermi level takes the shape of an upper conical surface for the electrons and a ...
In certain materials the topological invariant can be changed when certain bulk energy bands invert due to strong spin-orbital coupling. At the interface between an insulator with non-trivial topology, a so-called topological insulator, and one with a trivial topology, the interface must become metallic.
English: Informally depicts a phase diagram of topological and trivial insulators. There is no path from the topological insulators to the trivial insulators without passing through conducting phases. The diagram depicts a Z_2 topological invariant, since there are only two "islands" of insulators.
Kane is notable for theoretically predicting the quantum spin Hall effect (originally in graphene) and what would later be known as topological insulators. [1] [2] He received the 2012 Dirac Prize, along with Shoucheng Zhang and Duncan Haldane, for their groundbreaking work on two- and three-dimensional topological insulators.
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Fractional Chern insulators (FCIs) are lattice generalizations of the fractional quantum Hall effect that have been studied theoretically since 1993 [1] and have been studied more intensely since early 2010. [2] [3] They were first predicted to exist in topological flat bands carrying Chern numbers. They can appear in topologically non-trivial ...