Tailoring Pure Valley-Zeeman Spin-Orbit Coupling in WSe_{2}-Encapsulated Monolayer Graphene.

Engineering proximity effects in twisted van der Waals heterostructures offers a powerful platform for designing electronic properties. While theoretical predictions of quantum interference in transition metal dichalcogenide-encapsulated graphene can selectively control the spin-orbit coupling component, experimental realizations have remained elusive. Here, we report pure valley-Zeeman spin-orbit coupling in monolayer graphene achieved by encapsulation between two parallel twisted WSe_{2} monolayers. We observed a symmetry-enforced reordering of Landau levels, which is driven by the competition between the fixed valley-Zeeman energy and the magnetic-field-dependent cyclotron energy. This reordering is characterized by a transition from symmetry-broken states in the quantum Hall effect to a restored fourfold degeneracy with integer or half-integer quantum Hall sequences. We also demonstrate the ability to completely quench the proximity spin-orbit coupling by tuning the encapsulated geometry.