Fig. 1: Illustration of momentum-to-real-space mapping of topological singularities.

a A pseudospin-1/2 honeycomb lattice with two sublattices A and B is excited with three vortex beams, each with topological charge l. b A pseudospin-1 Lieb lattice with three sites (A, B, C) per unit cell is excited with four vortex beams. These vortex beams excite modes around conical intersections at the corners of the Brillouin zone (lower right inset). The arrows circulating around the conical intersections illustrate winding of the Berry phase (π in HCL and 2π in Lieb lattice). Topological charge conversion from l to l + 2s is a consequence of the mapping of topological singularity from momentum to real space. It occurs when initial excitation with l = ±1 is optimally aligned for a given pseudospin state (a) s = ±1/2 in HCL, and (b) s = ±1 in Lieb lattice. c Illustration of similar excitation of a Berry curvature monopole in 3D momentum space, leading to generation of a topological charge in real space with vorticity along the direction of excitation. Small blue and red arrows depict opposite pseudospin states.