Yu-Shiba-Rusinov states in Van Hove superconductors

A magnetic impurity in a conventional superconductor gives rise to Yu-Shiba-Rusinov (YSR) bound states inside the superconducting energy gap.
We study YSR states in two-dimensional superconductors with Fermi level tuned to a Van Hove singularity in the energy dispersion. We find that YSR states in real space inherit the anisotropy of the Van Hove saddle point, exhibiting divergence along radial spikes. We obtain an analytical expression for the local density of states in a minimal continuum model containing a Van Hove point, and confirm it in tight-binding lattice calculations.
Additionally, using lattice models relevant for transition metal dichalcogenides we discuss the long-range YSR states observable by scanning tunneling spectroscopy.