  Spin-orbit coupling (SOC) and electron-electron interaction can mutually
influence each other and give rise to a plethora of intriguing phenomena in
condensed matter systems. In pristine bilayer graphene, which has weak SOC,
intrinsic Lifshitz transitions and concomitant van-Hove singularities lead to
the emergence of many-body correlated phases. Layer-selective SOC can be
proximity induced by adding a layer of tungsten diselenide (WSe2) on its one
side. By applying an electric displacement field, the system can be tuned
across a spectrum wherein electronic correlation, SOC, or a combination of both
dominates. Our investigations reveal an intricate phase diagram of
proximity-induced SOC-selective bilayer graphene. Not only does this phase
diagram include those correlated phases reminiscent of SOC-free doped bilayer
graphene, but it also hosts unique SOC-induced states allowing a compelling
measurement of valley g-factor and a seemingly impossible correlated insulator
at charge neutrality, thereby showcasing the remarkable tunability of the
interplay between interaction and SOC in WSe2 enriched bilayer graphene.
