  Electrochemical intercalation is a powerful method for tuning the electronic
properties of layered solids. In this work, we report an electro-chemical
strategy to controllably intercalate lithium ions into a series of van der
Waals (vdW) heterostructures built by sandwiching graphene between hexagonal
boron nitride (h-BN). We demonstrate that encapsulating graphene with h-BN
eliminates parasitic surface side reactions while simultaneously creating a new
hetero-interface that permits intercalation between the atomically thin layers.
To monitor the electrochemical process, we employ the Hall effect to precisely
monitor the intercalation reaction. We also simultaneously probe the
spectroscopic and electrical transport properties of the resulting
intercalation compounds at different stages of intercalation. We achieve the
highest carrier density $> 5 \times 10^{13} cm^{-2}$ with mobility $> 10^3
cm^2/(Vs)$ in the most heavily intercalated samples, where Shubnikov-de Haas
quantum oscillations are observed at low temperatures. These results set the
stage for further studies that employ intercalation in modifying properties of
vdW heterostructures.
