Anti-higher-order Weyl semimetal

Abstract

Higher-order topology extends the bulk-boundary correspondence by enabling corner or hinge localized states. Here we identify an anti-higher-order Weyl semimetal, a three dimensional topological phase in which the conventional boundary hierarchy is reversed. Unlike conventional higher-order Weyl semimetals where bulk topology enforces hinge Fermi arcs, this phase hosts anti-hinge states, meaning the bulk topology forces states to vanish at specific hinge orientations. Using a minimal two-band model, we show how Weyl points separate the Brillouin zone into quantum anomalous Hall and anti-higher-order topological insulating regions, with the latter characterized by a band-inversion surface enclosing two distinct high-symmetry points carrying opposite topological charges. Analytical solutions for Weyl points, Berry curvature monopoles, and slice Chern numbers are derived, with numerical simulations confirming the resulting anti-hinge behavior. Our work establishes anti-higher-order topology as a dual counterpart to conventional higher-order phenomena, further extending the exploration of topological phases.