Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals

We give a bulk-hinge correspondence for higher-order topological phases protected by rotoinversion C4I symmetry in magnetic systems. Our approach allows us to show the emergence of the chiral hinge modes only from the information of the C4I eigenvalues at the high-symmetry points in the Brillouin zone. In addition, based on the bulk-hinge correspondence, we propose a class of higher-order Weyl semimetals (HOWSMs) being Weyl semimetals with hinge modes and Fermi-arc surface states. The HOWSM is characterized by topological invariants for three-dimensional higher-order topological insulators, and the topological invariants are determined by the C4I-symmetry eigenvalues at the high-symmetry points. This HOWSM has chiral hinge modes as a direct consequence of the three-dimensional higher-order topology in the bulk.