Probing a divergent van Hove singularity of graphene with a Ca 2 N support: A layered electride as a solid-state dopant

Layered electrides, as typified by ${\mathrm{Ca}}_{2}\mathrm{N}$, are unconventional quasi-two-dimensional metals with low work functions, in which the conduction electrons are localized between the cation layers as well as outside the surface. We have investigated the electronic structure of the interface between a layered electride and another material, using graphene on ${\mathrm{Ca}}_{2}\mathrm{N}$ as an example. Our first-principles calculation shows that a graphene layer on ${\mathrm{Ca}}_{2}\mathrm{N}$ remains flat and is doped to an extremely high density of $n=5\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ with its Fermi level (${E}_{F}$) aligned with the logarithmically divergent van Hove singularity (VHS) at a saddle point of graphene's ${\ensuremath{\pi}}^{*}$ band. This finding shows that graphene/${\mathrm{Ca}}_{2}\mathrm{N}$ is an ideal testing ground for the exploration of the many-body ground states, most notably superconducting states ($p+ip$ wave, $d$ wave, and $f$ wave), predicted to appear when ${E}_{F}$ is close to a VHS. The work function decreases abruptly upon monolayer attachment but reverts to that of ${\mathrm{Ca}}_{2}\mathrm{N}$ upon bilayer attachment. This peculiar behavior is explained in terms of the distinctive electronic structures of the constituent materials and their bonding.