Square-root higher-order Weyl semimetals

Abstract

The mathematical foundation of quantum mechanics is built on linear algebra, while the application of nonlinear operators can lead to outstanding discoveries under some circumstances. In this Letter, we propose a model of square-root higher-order Weyl semimetal (SHOWS) by inheriting features from its parent Hamiltonians. It is found that the SHOWS hosts both "Fermi-arc" surface and hinge states that connect the projection of the Weyl points. We theoretically construct and experimentally observe the exotic SHOWS state in three-dimensional (3D) stacked electric circuits with honeycomb-kagome hybridizations and double-helix interlayer couplings. Our results open the door for realizing the square-root topology in 3D solid-state platforms.

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• Higher-Order Topological Insulator on a Martini Lattice and Its Square Root Descendant
• Competition of non-Hermitian skin effect and topological localization of corner states observed in circuits
• Topological $n$-root Su-Schrieffer-Heeger model in a non-Hermitian photonic ring system
• Multiplicative topological semimetals
• Crystalline-electromagnetic responses of higher order topological semimetals
• Topological semimetal with coexisting nodal points and nodal lines
• Exceptionally deficient topological square-root insulators
• Floquet composite Dirac semimetals
• High-root topological edge-state bands
• Exceptional horns in $n$-root graphene and Lieb photonic ring lattices
• Anti-higher-order Weyl semimetal