  Layered electrides, as typified by Ca$_2$N, are a new class of
quasi-two-dimensional materials with low work functions. Using first-principles
calculations, we have shown that a graphene layer deposited on Ca$_2$N is doped
to $n=5\times 10^{14}$ cm$^{-2}$ with its Fermi level aligned with the
logarithmically divergent van Hove singularity in the graphene $\pi^*$ band.
For bilayer graphene on Ca$_2$N, the inner graphene layer is doped to the same
level, while the doping of the outer graphene layer is much more modest. This
finding opens an interesting possibility of using layered electrides for the
exploration of van Hove physics. The work function changes nonmonotonically
with the number of graphene layers, which we explain in terms of the peculiar
electronic structures of the constituent materials and their bonding.
