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Mechanical Weyl Modes in Topological Maxwell Lattices

Topological mechanical structures exhibit robust properties protected by topological invariants. In this letter, we study a family of deformed square lattices that display topologically protected zero-energy bulk modes analogous to the massless fermion modes of Weyl semimetals. Our findings apply to sufficiently complex lattices satisfying the Maxwell criterion of equal numbers of constraints and degrees of freedom. We demonstrate that such systems exhibit pairs of oppositely charged Weyl points, corresponding to zero-frequency bulk modes, that can appear at the origin of the Brillouin zone and move away to the zone edge (or return to the origin) where they annihilate. We prove that the existence of these Weyl points leads to a wavenumber-dependent count of topological mechanical states at free surfaces and domain walls.