Hybrid-order Weyl semimetal and its acoustic realizations

Abstract Hybrid-order topological insulators combine first- and higher-order topological properties and host topological boundary states with codimension one and more than one in different bandgaps. A Weyl semimetal (WSM) can possess two types of Weyl points: one class of Weyl points terminates the Fermi arc surface states, while another class of Weyl points not only launch Fermi arc surface states but also hinge arc states, exhibiting the hybrid-order topology. Here, we propose a hybrid-order WSM by stacking two-dimensional rhomboid lattices based on chiral nearest-neighbor and double-helix next-nearest interlayer couplings. The first type of Weyl point that only truncates the Fermi arc surface states exists at the crossing of any two-fold degeneracy of two adjacent bands, and the second type of Weyl point that connects the hinge arc states only appears at the crossing of the two middle bands. Our findings enrich the classification of topological semimetals in condensed matter physics.