Periodic table for topological insulators and superconductors

By Alexei Y. Kitaev. 2009

1,239 citations recorded by the source corpus.

Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds to one of the 2 types of complex and 8 types of real Clifford algebras. The phases within a given class are further characterized by a topological invariant, an element of some Abelian group that can be 0, Z, or Z_2. The interface between two infinite phases with different topological numbers must carry some gapless mode. Topological properties of finite systems are described in terms of K-homology. This classification is robust with respect to disorder, provided electron states near the Fermi energy are absent or localized. In some cases (e.g., integer quantum Hall systems) the K-theoretic classification is stable to interactions, but a counterexample is also given.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/96fbf2265785c08de5252f6178666fa80a8ddde2

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In Atomic and Molecular Physics, and Optics

1. Nathan Goldman
2. K. Kawabata
3. A. Amo
4. T. Ozawa
5. Hsin Lin
6. Arun Bansil
7. Tanmoy Das
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Citations in the corpus

• Topological insulators and superconductors (2010, positive): “Therefore, such a superconducting phase is topologically protected in the presence of TR symmetry, and can be described by aZ2 topological quantum number (Kitaev, 2009; Qiet al., 2009; Roy, 2008; Schnydert al., 2008).”
• Topological superconductors: a review (2016, neutral): “In Table III, we show the topological periodic table [9, 10] relevant to superconductors (a part of this table was already shown in Table I).”
• Classification of Interacting Topological Floquet Phases in One Dimension (2016, neutral): “After reviewing some ideas and explicit models for non-interacting Fermion Floquet SPTs[6, 8, 9, 25], we then address the modification of the fermionic Floquet SPT classification due to interactions in all of the non-trivial classes of the 10-fold way[28, 29].”
• Topological phases of fermions in one dimension (2010, neutral): “First, assume that we do not impose T : there are then two distinct phases of the Majorana chain [2]: the trivial phase”
• Topological Classification of Crystalline Insulators through Band Structure Combinatorics (2016, neutral): “The tenfold periodic table has been a cornerstone in the description of the connection between topology and symmetry [7,8].”
• Kitaev materials (2017, neutral): “Keeping in mind that the Kitaev model reduces to a free (Majorana) fermion model, this scenario can be rationalized by considering the classification of topological insulators [171, 172, 173] rooted in the symmetry classification of free-fermion systems [174].”
• Topological photonics (2014, neutral): “A large table of symmetry-protected topological phases have been theoretically classified [73, 74].”