Investigating the Cuprates as a platform for high-order Van Hove singularities and flat-band physics

Beyond the two-dimensional saddle-point Van Hove singularities (VHSs) with logarithmic divergences in the density of states, recent studies have identified higher-order VHSs with faster-than-logarithmic divergences that can amplify electron correlation effects. Here we show that the cuprate high-Tc superconductors harbor high-order VHSs in their electronic spectra and unveil a new correlation that the cuprates with high-order VHSs display higher Tc's. Our analysis indicates that the normal and higher-order VHSs can provide a straightforward new marker for identifying propensity of a material toward the occurrence of correlated phases such as the excitonic insulators and supermetals. Our study suggests cuprates and related high-Tc superconductors as materials for exploring the interplay between high-order VHSs, superconducting transition temperatures, and electron correlation effects. High-order Van Hove singularities (hoVHSs) with power-law divergences in the density-of-states are drawing current interest mainly in context of two-dimensional (2D) twisted moire materials. Using cuprate high-Tc superconductors as an example, here the authors illustrate complications that can arise in bulk materials in defining hoVHSs and the need to extend the definition of hoVHSs to include flat-band materials.