Periodic Clifford symmetry algebras on flux lattices

Abstract

Real 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 $\pi$ 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 novel topological states by various dimerization patterns, including a $3$D higher-order semimetal state with double-charged bulk nodal loops and hinge modes, a $4$D nodal surface semimetal with $3$D surface solid-ball zero modes, and $4$D Möbius topological insulators with a eightfold surface nodal point or a fourfold surface nodal ring. Our theory can be experimentally realized in artificial crystals by their engineerable ${\mathbb{Z}}_2$ gauge fields and capability to simulate higher dimensional systems.

8 pages, 6 figures

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Cited by in corpus (5)

• Demonstration of acoustic high-order Stiefel-Whitney semimetal in bilayer graphene sonic crystals
• Higher-order Klein bottle topological insulator in three-dimensional acoustic crystals
• Projective symmetry determined topology in flux Su-Schrieffer-Heeger model
• Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry
• Floquet Möbius topological insulators