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Van der Waals interactions with transition metal dichalcogenides was shown toinduce strong spin-orbit coupling (SOC) in graphene, offering great promises tocombine large experimental flexibility of graphene with unique tuningcapabilities of the SOC that can rotate spin by moving electrons or vice versa.Here, we probe SOC-driven band splitting and electron dynamics in graphene onWSe$_2$ by measuring ballistic transverse magnetic focusing. We found a clearsplitting in the first focusing peak whose evolution in charge density andmagnetic field is well reproduced by calculations using SOC strength of ~13 meVand no splitting in the second peak that indicates stronger Rashba SOC. Apossible suppression of electron-electron scatterings was also found intemperature dependence measurement. Further, we found that Shubnikov-de Haasoscillations exhibit SOC strength of ~3.4 meV, suggesting that it probesdifferent electron dynamics, calling for new theory. Our study demonstrates aninteresting possibility to exploit ballistic electron motion pronounced ingraphene for emerging spin-orbitronics.

Ballistic transport spectroscopy of spin-orbit-coupled bands in monolayer graphene on WSe$_2$