homotopy theory, (∞,1)-category theory, homotopy type theory
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see also algebraic topology
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A topological insulator is a topological state of matter which behaves as insulator in the bulk but has conducting edge states on the surface. More specifically, it is $U(1)$ and time reversal symmetry protected state of matter with trivial topological order, which behaves as an insulator in the bulk but has conducting edge states on the surface if the time reversal symmetry is not broken on the surface.
The topological insulator in 2D exhibiting a quantum spin Hall effect has been first proposed in
(In fact, none of the above materials have quantum spin Hall effect since the spin is not conserved due to the spin-orbital interaction that makes those materials non trivial.)
Ricardo Kennedy, Charles Guggenheim, Homotopy theory of strong and weak topological insulators, arxiv/1409.2529
L. Wu et al. Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator, Science (2016). doi
Last revised on February 12, 2020 at 04:32:23. See the history of this page for a list of all contributions to it.