  We study a system composed of graphene decorated with an array of islands
with C_3v symmetry that induce quantum dot (IQD) regions via proximity effects
and give rise to several spin-orbit couplings (SOCs). We evaluate transport
properties for an array of IQDs and analyze the conditions for realizing
isolated valley conductances and valley-state localization. The resulting
transmission shows a square-type behavior with wide gaps that can be tuned by
adjusting the strength of the staggered intrinsic SOCs. Realistic proximity
effects are characterized by weak SOC strengths, and the analysis of our
results in this regime shows that the Rashba coupling is the important
interaction controlling valley properties. As a consequence, a top gate voltage
can be used to tune the valley polarization and switch the valley scattering
for positive or negative incident energies. A proper choice of SOC strengths
leads to higher localization of valley states around the linear array of IQDs.
These systems can be implemented in heterostructures composed of graphene and
semiconducting transition-metal dichalcogenides (TMDs) such as MoSe2, WSe2,
MoS2, or WS2. In these setups, the magnitudes of induced SOCs depend on the
twist angle, and due to broken valley degeneracy, valley-polarized currents at
the edges can be generated in a controllable manner as well as localized valley
states. Our findings suggest an alternative approach for producing
valley-polarized currents and propose a corresponding mechanism for
valley-dependent electron optics and optoelectronic devices.
