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Valley-related multiple Hall effect in 2D lattice is a fundamental transportphenomenon in the fields of condensed-matter physics and material science. Sofar, most proposals for its realization are limited to toy models or extrinsiceffects. Here, based on tight-binding model and first-principles calculations,we report the discovery of intrinsic valley-related multiple Hall effect in 2Dorganometallic lattice of NbTa-benzene. Protected by the breaking of bothtime-reversal and inversion symmetry, NbTa-benzene exhibits large valleypolarization spontaneously in both the conduction and valence bands,guaranteeing the anomalous valley Hall effect. Simultaneously, because of theexchange interaction and strong spin-orbit coupling, intrinsic band inversionoccurs at one valley, which ensures the valley-polarized quantum anomalous Halleffect, thus presenting the extraordinary valley-related multiple Hall effectin nature. In addition, it can be transformed into the phase with ferrovalleyor quantum anomalous Hall effect solely through strain engineering. Theseinsights not only are useful for the fundamental research in valley-relatedphysics, but also enable a wide range of novel device applications.

Intrinsic Valley-Related Multiple Hall Effect in 2D Organometallic Lattice