Classification of Critical Points in Energy Bands Based on Topology, Scaling and Symmetry

TL;DR

This paper introduces a new classification scheme for high-order critical points in energy bands, extending beyond traditional van Hove singularities, with implications for tuning electronic properties via external parameters.

Contribution

It provides a topological, scaling, and symmetry-based classification of high-order critical points, revealing their divergent DOS and tunability at generic or symmetric momenta.

Findings

High-order critical points can exhibit power-law divergent DOS.

Such critical points can be realized at generic or symmetric momenta.

External parameters like twist angle and strain can tune these critical points.

Abstract

A critical point of the energy dispersion is the momentum where electron velocity vanishes. At the corresponding energy, the density of states (DOS) exhibits non-analyticity such as divergence. Critical points can be first classified as ordinary and high-order ones, and the ordinary critical points have been studied thoroughly by L\'eon van Hove. In this work, we describe and classify high-order critical points based on topology, scaling and symmetry, which are beyond L\'eon van Hove's framework. We show that high-order critical points can have power-law divergent DOS with particle-hole asymmetry, and can be realized at generic or symmetric momenta by tuning a few parameters such as twist angle, strain, pressure and/or external fields.