Weyl superconductors feature Weyl points at zero energy in the three-dimensional Brillouin zone and arc states that connect the projections of these Weyl points on the surface. We report that higher-order Weyl superconductors can be realized in odd-parity topological superconductors with time-reversal symmetry being broken by periodic driving. Different from conventional Weyl points, the higher-order Weyl points in the bulk separate 2D first- and second-order topological phases, while on the surface, their projections are connected not only by conventional surface Majorana arcs but also by hinge Majorana arcs. Strikingly, without the protection by a Chern number, the hinge Majorana arcs are anisotropic with respect to surface orientations, forcing a different connectivity of Weyl points for a rotated surface. We identify such anisotropic Weyl-point connectivity as a characteristic feature of higher-order Weyl materials. Moreover, with time-reversal symmetry being broken, the higher-order hinge Majorana arcs are spin polarized, which offers a promising opportunity to observe the anisotropic Weyl-point connectivity with spin-sensitive probes. Besides condensed-matter systems, we provide a feasible experimental setup for realizing our predictions in cold-atom systems.

• Received 21 September 2020
• Revised 21 February 2021
• Accepted 19 April 2021

DOI:https://doi.org/10.1103/PhysRevB.103.184510