Time-Reversal Even Charge Hall Effect from Twisted Interface Coupling

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