Designer spin-orbit superlattices: symmetry-protected Dirac cones and spin Berry curvature in two-dimensional van der Waals metamaterials

Abstract

The emergence of strong relativistic spin-orbit effects in low-dimensional systems provides a rich opportunity for exploring unconventional states of matter. Here, we present a route to realise tunable relativistic band structures based on the lateral patterning of proximity-induced spin-orbit coupling. The concept is illustrated on a patterned graphene–transition metal dichalcogenide heterostructure, where the spatially periodic spin-orbit coupling induces a rich mini-band structure featuring massless and massive Dirac bands carrying large spin Berry curvature. The envisaged systems 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 findings open pathways to two-dimensional quantum material design and low-power spintronic applications. Engineering sizeable spin-orbit coupling (SOC) in graphene generates effects unmatched in traditional low-dimensional systems. Here, the authors show that the periodic modulation of SOC in 1D patterned graphene heterostructures leads to unusual mini-band structures with symmetry-protected Dirac cones featuring enhanced spin Berry curvature, which paves the way to tunable spin Hall responses.