The low nuclear spin density and weak spin-orbit coupling make graphene – a two-dimensional crystal of carbon – an interesting material to study and probe the coherence and dynamics the spins of (pseudo-) Dirac electrons . Among the interesting challenges is the confinement of effectively massless particles in a gapless semiconductor (or semimetal) e.g. in graphene nanoribbons  or bilayer graphene [2,3]. Quantum dots in graphene have been realized experimentally using nanostructured samples , as well as both of the above approaches to confinement [4-6]. In contrast to graphene, the monolayer transition-metal dichalcogenides (TMDCs) constitute two-dimensional semiconductors with a finite band gap and a relatively strong spin-orbit coupling. Spin-related (and other) properties of these materials can be studied with a symmetry-based effective Hamiltonian approach combined with k.p theory [7-9]. It is interesting that spin-orbit coupling can turn graphene into a topological insulator , but the intrinsic spin-orbit interaction is too weak to open a noticeable topological gap. We explore the induced spin-orbit coupling in graphene combined with TMDCs in twisted van der Waals heterostructures  and found an interesting twist-angle dependent induced spin-orbit coupling (see Figure).
Figure (a) Twisted graphene-TMDC heterostructure with inter-layer separation d⊥. (b) The twist angle θ controls the induced spin-orbit coupling λVZ in graphene  around the K (-K) point, shown in blue (orange). Dashed black line: exact diagonalization at the K point.
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