Graphene under lateral spin-orbit superlattices: symmetry- protected Dirac cones and hot spots of spin Berry Curvature in 2D van der Waals metamaterials.

Proximity effects in two-dimensional materials have provided unique opportunities for basic condensed matter physics to obtain an understanding of emergent electronic properties that otherwise are unachiev- able. Here, we present a route to realize tunable relativistic band structures based on the lateral patterning of proximity-induced spin-orbit coupling. The concept is illustrated on lateral superlattice fabricated from graphene and transition metal dichalcogenide monolayers, where the spatially periodic spin-orbit coupling induces a rich mini-band structure featuring massless and massive Dirac bands carrying large spin Berry curvature [1]. The envisaged superlattices support robust and gate-tunable spin Hall responses driven by the quantum geometry of mini-bands, which can be tailored through metasurface fabrication methods and twisting effects. These fndings open pathways to two-dimensional quantum material design and low-power spintronic applications. [1] Martelo, L.M., Ferreira, A. Designer spin-orbit superlattices: symmetry-protected Dirac cones and spin Berry curvature in two-dimensional van der Waals metamaterials. Commun. Phys. 7, 308 (2024). https://doi.org/10.1038/s42005-024-01801-8. We acknowledge FCT-Portugal through Grant No. UID/04650 - Centro de Física das Universidades do Minho e do Porto.