Super Van Hove singularities in cuprate high-T_c superconductors

Two-dimensional (2D) Van Hove singularities (VHSs) associated with the saddle point extrema of the energy dispersions usually yield logarithmic divergences in the density of states (DOS). However, recent studies find that the VHSs associated with higher-order saddle-points yield faster-than-logarithmic divergences which can amplify electron correlation effects and create exotic states such as the supermetals in 2D materials.[1] Here we discuss the existence of high-order VHSs in the cuprate high-Tc superconductors and show how these VHSs are the result of the effective electronic dimensionality of the material being smaller than the dimensionality of the crystal lattice.[2] The presence of high-order VHSs is found to be correlated with the occurrence of higher Tc’s in the cuprates. We also comment on the role of higher-order VHSs in generating complex intertwined magnetic, charge-order, and superconducting phases.
[1] F. Noah, Q. Yuan, Hiroki Isobe, and Liang Fu, Nat. Commun. 10, 5769 (2019).
[2] R.S. Markiewicz, I.G. Buda, P. Mistark, C. Lane, and A. Bansil, Scientific Reports 7, 44008 (2017).