  Twist-engineering of the electronic structure of van-der-Waals layered
materials relies predominantly on band hybridization between layers. Band-edge
states in transition-metal-dichalcogenide semiconductors are localized around
the metal atoms at the center of the three-atom layer and are therefore not
particularly susceptible to twisting. Here, we report that high-lying excitons
in bilayer WSe2 can be tuned over 235 meV by twisting, with a twist-angle
susceptibility of 8.1 meV/{\deg}, an order of magnitude larger than that of the
band-edge A-exciton. This tunability arises because the electronic states
associated with upper conduction bands delocalize into the chalcogenide atoms.
The effect gives control over excitonic quantum interference, revealed in
selective activation and deactivation of electromagnetically induced
transparency (EIT) in second-harmonic generation. Such a degree of freedom does
not exist in conventional dilute atomic-gas systems, where EIT was originally
established, and allows us to shape the frequency dependence, i.e. the
dispersion, of the optical nonlinearity.
