Strain can be used to modify the band structure—and thus the electronic properties—of two-dimensional materials. However, research has focused on the use of monolayer graphene with a limited lowering of spatial symmetry and considered only the real-space pseudo-magnetic field. Here we show that lithographically patterned strain can be used to create a non-trivial band structure and exotic phase of matter in bilayer graphene. The approach creates artificially corrugated bilayer graphene in which real-space and momentum-space pseudo-magnetic fields (Berry curvatures) coexist and have non-trivial properties, such as Berry curvature dipoles. This leads to the appearance of two Hall effects without breaking time-reversal symmetry: a nonlinear anomalous Hall effect that originates from the Berry curvature dipole, previously only observed in the Weyl semimetal WTe2, and a linear Hall effect that originates from a warped band dispersion on top of Rashba-like valley–orbit coupling and is similar to the recently proposed Magnus Hall effect.
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