Layer Coherence Origin of Planar Hall Effect: From Charge to Multipole and Valley.

We uncover a new origin of the planar Hall effect, as an intrinsic property of layer coherent electrons, that exists even in bilayer and trilayer atomically thin limits. It reforms the existing theories requiring three-dimensional orbital motion or strong spin-orbit coupling of certain forms, which are absent in van der Waals thin films. We exemplify that the effect can be triggered by strain and interlayer sliding in twisted structures with rich tunability and strong magnitudes. Furthermore, this layer coherence mechanism broadens the conceptual framework to include the planar multipole Hall effect and valley Hall effect induced by the in-plane pseudomagnetic field, outreaching the existing mechanisms. The layer mechanism also provides a new route toward quantized Hall response upon a topological phase transition induced by the in-plane magnetic field. These results unveil the unexplored potential of quantum layertronics and moiré flat bands for planar transport in 2D materials.