Composite multi-vortex diffraction-free beams and van Hove singularities in honeycomb lattices

We find diffraction-free beams for graphene and MoS\(_2\)-type honeycomb optical lattices. The resulting composite solutions have the form of multi-vortices, with spinor topological charges (\(n\), \(n\pm1\)). Exact solutions for the spinor components are obtained in the Dirac limit. The effects of the valley degree of freedom and the mass are analyzed. Passing through the van-Hove singularity the topological structure of the solutions is modified. Exactly at the singularity the diffraction-free beams take the form of strongly localized one-dimensional stripes.