Optical absorption signatures of superconductivity driven by Van Hove singularities

Van Hove singularities (VHS) near Fermi level are known to be a candidate driving the superconductivity observed in various two-dimensional systems, such as graphene-based few-layer systems and Kagome superconductors. Although the divergence of density of states (DOS) at VHS gives rise to unique superconducting properties, the character of VHS such as the degree of divergence is often unclear in experiments. In this work, we theoretically show that the presence and absence of the optical absorption peak driven by an applied current in different directions can be used to experimentally deduce the directionality and dispersion of relevant VHS. For a conventional VHS with logarithmic diverging DOS, the finite AC absorption is prohibited by the momentum conservation even in superconducting states. For a higher-order VHS whose DOS has a stronger power-law divergence, we find the absorption peak across the superconducting gap along a certain direction. Our study suggests the longitudinal optical conductivity as a possible signature to distinguish and identify these two types of VHS. I will discuss concrete experimental schemes in Kagome metal, AV$_3$Sb$_5$ (A=K, Rb, Cs).