Physics

Mathematical optimization

Bilayer graphene

Van Hove singularity

Electron

Singularity

Geometry

Saddle point

Condensed matter physics

Saddle

Graphene

Mathematics

Fermi level

Density of states

Quantum mechanics

Nature Communications

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.

Magic of high-order van Hove singularity