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Article: Periodic Clifford symmetry algebras on flux lattices

TitlePeriodic Clifford symmetry algebras on flux lattices
Authors
Issue Date2022
Citation
Physical Review B, 2022, v. 106, n. 12, article no. 125102 How to Cite?
AbstractReal Clifford algebras play a fundamental role in the eight real Altland-Zirnbauer symmetry classes and the classification tables of topological phases. Here, we present another elegant realization of real Clifford algebras in the d-dimensional spinless rectangular lattices with π flux per plaquette. Due to the T-invariant flux configuration, real Clifford algebras are realized as projective symmetry algebras of lattice symmetries. Remarkably, d mod 8 exactly corresponds to the eight Morita equivalence classes of real Clifford algebras with eightfold Bott periodicity, resembling the eight real Altland-Zirnbauer classes. The representation theory of Clifford algebras determines the degree of degeneracy of band structures, both at generic k points and at high-symmetry points of the Brillouin zone. Particularly, we demonstrate that the large degeneracy at high-symmetry points offers a rich resource for forming topological states by various dimerization patterns, including a three-dimensional (3D) higher-order semimetal state with double-charged bulk nodal loops and hinge modes, a 4D nodal surface semimetal with 3D surface solid-ball zero modes, and 4D Möbius topological insulators with an eightfold surface nodal point or a fourfold surface nodal ring. Our theory can be experimentally realized in artificial crystals by their engineerable Z2 gauge fields and capability to simulate higher-dimensional systems.
Persistent Identifierhttp://hdl.handle.net/10722/335044
ISSN
2023 Impact Factor: 3.2
2023 SCImago Journal Rankings: 1.345
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorHuang, Yue Xin-
dc.contributor.authorChen, Z. Y.-
dc.contributor.authorFeng, Xiaolong-
dc.contributor.authorYang, Shengyuan A.-
dc.contributor.authorZhao, Y. X.-
dc.date.accessioned2023-10-24T08:28:41Z-
dc.date.available2023-10-24T08:28:41Z-
dc.date.issued2022-
dc.identifier.citationPhysical Review B, 2022, v. 106, n. 12, article no. 125102-
dc.identifier.issn2469-9950-
dc.identifier.urihttp://hdl.handle.net/10722/335044-
dc.description.abstractReal Clifford algebras play a fundamental role in the eight real Altland-Zirnbauer symmetry classes and the classification tables of topological phases. Here, we present another elegant realization of real Clifford algebras in the d-dimensional spinless rectangular lattices with π flux per plaquette. Due to the T-invariant flux configuration, real Clifford algebras are realized as projective symmetry algebras of lattice symmetries. Remarkably, d mod 8 exactly corresponds to the eight Morita equivalence classes of real Clifford algebras with eightfold Bott periodicity, resembling the eight real Altland-Zirnbauer classes. The representation theory of Clifford algebras determines the degree of degeneracy of band structures, both at generic k points and at high-symmetry points of the Brillouin zone. Particularly, we demonstrate that the large degeneracy at high-symmetry points offers a rich resource for forming topological states by various dimerization patterns, including a three-dimensional (3D) higher-order semimetal state with double-charged bulk nodal loops and hinge modes, a 4D nodal surface semimetal with 3D surface solid-ball zero modes, and 4D Möbius topological insulators with an eightfold surface nodal point or a fourfold surface nodal ring. Our theory can be experimentally realized in artificial crystals by their engineerable Z2 gauge fields and capability to simulate higher-dimensional systems.-
dc.languageeng-
dc.relation.ispartofPhysical Review B-
dc.titlePeriodic Clifford symmetry algebras on flux lattices-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1103/PhysRevB.106.125102-
dc.identifier.scopuseid_2-s2.0-85138454347-
dc.identifier.volume106-
dc.identifier.issue12-
dc.identifier.spagearticle no. 125102-
dc.identifier.epagearticle no. 125102-
dc.identifier.eissn2469-9969-
dc.identifier.isiWOS:000855024100003-

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