  We study the effects of heterostrain on moir\'e bands in twisted bilayer
graphene and bilayer transition metal dichalcogenide (TMD) systems. For bilayer
graphene with twist angle near $1^\circ$, we show that heterostrain
significantly increases the energy separation between conduction and valence
bands as well as the Dirac velocity at charge neutrality, which resolves
several puzzles in scanning tunneling spectroscopy and quantum oscillation
experiments at once. For bilayer TMD, we show that applying small heterostrain
generally leads to flat moir\'e bands that are highly tunable.

Materials Science;Strongly Correlated Electrons