Origin and Magnitude of 'Designer' Spin-Orbit Interaction in Graphene on Semiconducting Transition Metal Dichalcogenides

We use a combination of experimental techniques to demonstrate a general occurrence of spin-orbit interaction (SOI) in graphene on transition metal dichalcogenide (TMD) substrates. Our measurements indicate that SOI is ultrastrong and extremely robust, despite it being merely interfacially induced, with neither graphene nor the TMD substrates changing their structure. This is found to be the case irrespective of the TMD material used, of the transport regime, of the carrier type in the graphene band, or of the thickness of the graphene multilayer. Specifically, we perform weak antilocalization (WAL) measurements as the simplest and most general diagnostic of SOI, and we show that the spin relaxation time is very short (approximately 0.2 ps or less) in all cases regardless of the elastic scattering time, whose value varies over nearly 2 orders of magnitude. Such a short spin-relaxation time strongly suggests that the SOI originates from a modification of graphene band structure. We confirmed this expectation by measuring a gate-dependent beating, and a corresponding frequency splitting, in the low-field Shubnikov-de Haas magnetoresistance oscillations in high-quality bilayer graphene devices on WSe2. These measurements provide an unambiguous diagnostic of a SOI-induced splitting in the electronic band structure, and their analysis allows us to determine the SOI coupling constants for the Rashba term and the so-called spin-valley coupling term, i.e., the terms that were recently predicted theoretically for interface-induced SOI in graphene. The magnitude of the SOI splitting is found to be on the order of 10 meV, more than 100 times greater than the SOI intrinsic to graphene. Both the band character of the interfacially induced SOI and its robustness and large magnitude make graphene-on-TMD a promising system to realize and explore a variety of spin-dependent transport phenomena, such as, in particular, spin-Hall and valley-Hall topological insulating states.