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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]
It indicates the mathematical group for the topological invariant of the topological insulators and topological superconductors, given a dimension and discrete symmetry class. [1] The ten possible discrete symmetry families are classified according to three main symmetries: particle-hole symmetry, time-reversal symmetry and chiral symmetry.
The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance R xy exhibits steps that take on the quantized values
In physics, Dirac cones are features that occur in some electronic band structures that describe unusual electron transport properties of materials like graphene and topological insulators. [1] [2] [3] In these materials, at energies near the Fermi level, the valence band and conduction band take the shape of the upper and lower halves of a ...
Two-dimensional topological insulators (also known as the quantum spin Hall insulators) with one-dimensional helical edge states were predicted in 2006 by Bernevig, Hughes and Zhang to occur in quantum wells (very thin layers) of mercury telluride sandwiched between cadmium telluride, [7] and were observed in 2007.
In fact topological insulators are different from topologically ordered states defined in this article. 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.
Topological plexcitons make use of the properties of TIs to achieve similar control over the direction of current flow. [3] Plexcitons were found to emerge from an organic molecular layer (excitons) and a metallic film (plasmons). Dirac cones appeared in the plexcitons' two-dimensional band-structure. An external magnetic field created a gap ...
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.