  Magic-angle twisted bilayer graphene exhibits quasi-flat low-energy bands
with Van Hove singularities close to the Fermi level. These singularities play
an important role in the exotic phenomena observed in this material, such as
superconductivity and magnetism, by amplifying electronic correlation effects.
In this work, we study the correspondence of four-terminal conductance and the
Fermi surface topology as a function of the twist angle, pressure, and energy
in mesoscopic, ballistic samples of small-angle twisted bilayer graphene. We
establish a correspondence between features in the wide-junction conductance
and the presence of van Hove singularities in the density of states. Moreover,
we identify additional transport features, such as a large, pressure-tunable
minimal conductance, conductance peaks coinciding with non-singular band
crossings, and unusually large conductance oscillations as a function of the
system size. Our results suggest that twisted bilayer graphene close the magic
angle is a unique system featuring simultaneously large conductance due to the
quasi-flat bands, strong quantum nonlinearity due to the Van Hove singularities
and high sensitivity to external parameters, which could be utilized in
high-frequency device applications and sensitive detectors.
