Classification of Topological Insulators and Superconductors
By A. Schnyder, S. Ryu, A. Furusaki, A. Ludwig. 2009
330 citations recorded by the source corpus.
An exhaustive classification scheme of topological insulators and superconductors is presented. The key property of topological insulators (superconductors) is the appearance of gapless degrees of freedom at the interface/boundary between a topologically trivial and a topologically non‐trivial state. Our approach consists in reducing the problem of classifying topological insulators (superconductors) in d spatial dimensions to the problem of Anderson localization at a (d−1) dimensional boundary of the system. We find that in each spatial dimension there are precisely five distinct classes of topological insulators (superconductors). The different topological sectors within a given topological insulator (superconductor) can be labeled by an integer winding number or a Z2 quantity. One of the five topological insulators is the “quantum spin Hall” (or: Z2 topological) insulator in d = 2, and its generalization in d = 3 dimensions. For each dimension d, the five topological insulators correspond to a certain ...
Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/0a0f4960c59a0b53cf4d1274e04d55eceef42761
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In Atomic and Molecular Physics, and Optics
In Materials Chemistry
Citations in the corpus
- Angle-resolved photoemission studies of quantum materials (2020, neutral): “The theory of topological superconductors is analogous to that of TIs, with the role of the insulating band gap replaced by the particle-hole symmetric superconducting gap (Qi and Zhang, 2011; Schnyder et al., 2009).”
- Topological photonics (2018, background): “…complete classification of noninteracting fermionic topological phases in any dimension based on the time-reversal, particle-hole, and chiral symmetries is known in the literature (Kitaev, Lebedev, and Feigelman, 2009; Schnyder et al., 2009; Ryu et al., 2010; Teo and Kane, 2010; Chiu et al., 2016).”
- K-Theory and Pseudospectra for Topological Insulators (2015, background): “Following Kitaev [22], we will focus on situations where there is a localized spectral gap.”
- Symmetry Indicators and Anomalous Surface States of Topological Crystalline Insulators (2017, methodology): “[3] Andreas P Schnyder, Shinsei Ryu, Akira Furusaki, and An-”