Zero-magnetic-field Hall effects in artificially corrugated bilayer graphene

The Hall effect family has been an important driving force behind the advance of solid-state physics and technology over the past century, e.g. the quantum Hall effect opened the door to explore the world of matter via topology and defined today's metrology standard, the anomalous Hall effect led to the discovery of the geometric properties of the wavefunctions now known as the Berry curvature and had a far-reaching impact on our understanding of quantum systems. Here, we demonstrate the nonlinear anomalous Hall effect (AHE) and a nontrivial pseudo-magnetoresistance anisotropy, which may be viewed as a new type of planar Hall effect, in a non-magnetic material at zero magnetic field, i.e. without breaking the time-reversal symmetry. Our findings challenge the general belief that the broken time-reversal symmetry is a necessary condition to have a nonvanishing Hall conductivity. Such Hall effects are observed in an artificially corrugated bilayer graphene system in which strain and interlayer coupling are specially engineered to induce pseudo-magnetic fields and break the spatial inversion symmetry. This creates tilted mini-Dirac cones with Rashba-like valley-orbit coupling and the momentum-space Berry curvature dipole, which are responsible for the pseudo-magnetoresistance anisotropy and nonlinear AHE, respectively. This new class of condensed-matter systems provides a unique platform to study novel geometrical and/or topological quantum phenomena when both the real-space and momentum-space pseudo-magnetic fields (Berry curvatures) exist. The capability to artificially create nontrivial band structure and Berry curvatures from conventional two-dimensional materials such as graphene via lithographically-patterned lattice deformation provides an alternative route to exotic phases of matter on par with the discovery of novel materials or engineering the band structure with twistronics.