  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.
