  We report the discovery of electric-field-induced transition from a
topologically trivial to a topologically nontrivial band structure in an
atomically sharp heterostructure of bilayer graphene (BLG) and single-layer
WSe2 per the theoretical predictions of Gmitra and Fabian [Phys. Rev. Lett.
119, 146401 (2017)]. Through detailed studies of the quantum correction to the
conductance in the BLG, we establish that the band-structure evolution arises
from an interplay between proximity-induced strong spin-orbit interaction (SOI)
and the layer polarizability in BLG. The low-energy carriers in the BLG
experience an effective valley Zeeman SOI that is completely gate tunable to
the extent that it can be switched on or off by applying a transverse
displacement field or can be controllably transferred between the valence and
the conduction band. We demonstrate that this results in the evolution from
weak localization to weak antilocalization at a constant electronic density as
the net displacement field is tuned from a positive to a negative value with a
concomitant SOI-induced splitting of the low-energy bands of the BLG near the K
(K') valley, which is a unique signature of the theoretically predicted
spin-orbit valve effect. Our analysis shows that quantum correction to the
Drude conductance in Dirac materials with strong induced SOI can only be
explained satisfactorily by a theory that accounts for the SOI-induced spin
splitting of the BLG low-energy bands. Our results demonstrate the potential
for achieving highly tunable devices based on the valley Zeeman effect in
dual-gated two-dimensional materials.
