High order Van Hove singularities and flat bands*

Beyond the two-dimensional (2D) saddle-point Van Hove singularities (VHSs) with logarithmic divergences in the density of states (DOS), recent studies have identified high-order VHSs with faster-than-logarithmic divergences that can amplify electron correlation effects [1-3]. Here we demonstrate a close relationship between the high-order VHSs and flat bands and show that this provides an estimate of the electronic dimensionality of the flat bands.  We find that 3D materials can host high-order VHSs with similar power-law divergences to those near the cuprates [3].

[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).

[3] R.S. Markiewicz, B. Singh, C. Lane, and A. Bansil, arXiv:2105.04546.