Quantum Anomalous\nLayer Hall Effect in Realistic van\nder Waals Heterobilayers

The\nquantum anomalous layer Hall effect (QALHE), characterized\nby the precise control of the quantum anomalous Hall effect on different\nlayers due to spin-layer-chirality coupling in van der Waals (vdW)\nlayered materials, is of great importance in both fundamental physics\nand nanodevices. In this work, through the analysis of a low-energy\neffective model for vdW heterobilayers under biaxial strain, we propose\nthe QALHE in valleytronic materials for the first time. The spin-layer-locked\nedge states and Chern numbers in heterobilayers give rise to dissipationless\ncurrents localized in specific layers, realizing the long-sought QALHE\nin heterobilayers. The switch of the chirality of edge states and\nChern numbers in heterobilayer systems can be achieved by applying\na biaxial strain. We have validated this mechanism in a series of\nrealistic valleytronic materials, including VSi<sub>2</sub>N<sub>4</sub>/VSiCN<sub>4</sub> and RuCl<sub>2</sub>/FeCl<sub>2</sub> heterobilayers.\nOur work reveals a new mechanism for achieving the QALHE with promising\n applications in spintronics and quantum layertronics.