Time-reversal even charge hall effect from twisted interface coupling.

Under time-reversal symmetry, a linear charge Hall response is usually deemed to be forbidden by the Onsager relation. In this work, we discover a scenario for realizing a time-reversal even linear charge Hall effect in a non-isolated two-dimensional crystal allowed by time reversal symmetry. The restriction by Onsager relation is lifted by interfacial coupling with an adjacent layer, where the overall chiral symmetry requirement is fulfilled by a twisted stacking. We reveal the underlying band geometric quantity as the momentum-space vorticity of layer current. The effect is demonstrated in twisted bilayer graphene and twisted homobilayer transition metal dichalcogenides with a wide range of twist angles, which exhibit giant Hall ratios under experimentally practical conditions, with gate voltage controlled on-off switch. This work reveals intriguing Hall physics in chiral structures, and opens up a research direction of layertronics that exploits the quantum nature of layer degree of freedom to uncover exciting effects.