Dirac branch-cut modes with relativistic transport
Emergent Dirac fields, exhibiting effective relativistic physics, are most commonly associated with bulk and surface states in materials such as graphene and topological insulators. Here we show that phase dislocations of a complex Dirac mass support a distinct family of propagating Dirac defect states that behave as massless or massive one-dimensional relativistic modes. These traveling-wave defect states, termed Dirac branch-cut (DBC) modes, are governed by a one-dimensional Dirac Hamiltonian whose effective mass is controlled by the phase difference across the branch cut. Using acoustic metamaterials, we experimentally demonstrate a range of relativistic phenomena exhibited by DBC modes, including relativistic dispersion, energy-independent confinement, Klein tunnelling, and transport along freeform (e.g., spiral) trajectories. Our results establish branch-cut defects as a distinct platform for realizing propagating Dirac defect states, extending relativistic Dirac physics from bulk and surface states to propagating modes confined to defect boundaries.