# Magic of high order van Hove singularity

## TL;DR

This paper introduces high-order van Hove singularities in two-dimensional materials, where saddle points lead to power-law divergences in the density of states, potentially enhancing electron correlation effects.

## Contribution

It presents the concept of high-order van Hove singularities and demonstrates how they can be realized in moiré superlattices through tuning parameters like twist angle or pressure.

## Key findings

- High-order van Hove singularities cause power-law divergence in density of states.
- Such singularities can be achieved in moiré materials by tuning a single parameter.
- Enhanced electron correlation effects are expected near these singularities.

## Abstract

We introduce a new type of van Hove singularity in two dimensions, where a saddle point in momentum space is changed from second-order to high-order. Correspondingly, the density of states near such ``high-order van Hove singularity'' is significantly enhanced from logarithmic to power-law divergence, which promises stronger electron correlation effects. High-order van Hove singularity can be generally achieved by tuning the band structure with a single parameter in moir\'e superlattices, such as twisted bilayer graphene by tuning twist angle or applying pressure, and trilayer graphene by applying vertical electric field.