  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.
