Two-dimensional higher-order Weyl semimetals

We propose a theoretical scheme to realize two-dimensional higher-order Weyl semimetals using a trilayer topological film coupled with a d-wave altermagnet. Our results show that the trilayer topological film exhibits two-dimensional Weyl semimetal characteristics with helical edge states. Notably, the Weyl points are located at four high-symmetry points in the Brillouin zone, and the topology of symmetry subspaces governs the formation of these Weyl points and edge states. Upon introducing a d-wave altermagnet oriented along the z-direction, gaps open in the helical edge states while preserving two Weyl points, leading to the realization of two-dimensional higher-order Weyl semimetals hosting topological corner states. The nonzero winding number in the subspace along the high-symmetry line serves as a topological invariant characterizing these corner states, and the other subspace Hamiltonian confirms the existence of the Weyl points. Finally, a topological phase diagram provides a complete topological description of the system.