  We demonstrate a new method to control the Fermi level around the van Hove
singularity (VHS) in Li-intercalated graphene on the SiC substrate. By
angle-resolved photoemission spectroscopy, we observed a clear Lifshitz
transition in the vicinity of the VHS by increasing the graphene thickness.
This behavior is unexpected in a free-standing Li-intercalated graphene model.
The calculation including the substrate suggests that the surface state
stabilizes the Fermi level around the VHS of the Dirac bands via hybridization.
In addition, we found that a sizable Schottky barrier is formed between
graphene and the substrate. These properties allow us to explore the electronic
phase diagram around the VHS by controlling the thickness and electric field in
the device condition.
