  Spin and angular momenta of light are important degrees of freedom in
nanophotonics which control light propagation, optical forces and information
encoding. Typically, optical angular momentum is generated using q-plates or
spatial light modulators. Here, we show that graphene-supported plasmonic
nanostructures with broken rotational symmetry provide a surprising spin to
orbital angular momentum conversion, which can be continuously controlled by
changing the electrochemical potential of graphene. Upon resonant illumination
by a circularly polarized plane wave, a polygonal array of indium-tin-oxide
nanoparticles on a graphene sheet generates scattered field carrying
electrically-tunable orbital angular momentum. This unique photonic spin-orbit
coupling occurs due to the strong coupling of graphene plasmon polaritons and
localised surface plasmons of the nanoparticles and leads to the controlled
directional excitation of graphene plasmons. The tuneable spin-orbit conversion
pave the way to high-rate information encoding in optical communications,
electric steering functionalities in optical tweezers, and nanorouting of
higher-dimensional entangled photon states.
