Valley higher-order Weyl semimetals

Higher-order topological phases have attracted much attention due to the rich topological modes localized at multidimensional boundaries. Here we propose valley higher-order Weyl semimetal phases in honeycomb lattices and suggest its realization in sonic crystals and discuss its possible candidates in other systems. Such topological semimetals host three-dimensional Weyl points in the bulk, two-dimensional Fermi-arc surface states on the surfaces, and one-dimensional hinge-arc states on hinges perpendicular to the hexagonal plane. All these states exhibit valley-contrasting physics in different dimensions (bulk, surfaces, and hinges) in a single physical system. Enriched by the emergent valley degree-of-freedom, these valley higher-order Weyl semimetals have unconventional properties that are appealing for the topological manipulation of wave propagation and hence the material properties and potential applications.