  Water confined between two graphene layers with a small separation forms a
two-dimensional ice structure,with an apparent square symmetry [Algara-Siller
et al., Nature (London) 519, 443 (2015)], which is poorly understood. A density
functional approach is applied to the water, but not to the water graphene
interactions, since the two crystals are incommensurate. We thus need use a
potential model for the interaction between water and graphene. We analyze the
models for confinement of water by graphene, and find that even though the
general features are well established, the detail is not so well understood.
Using a representative range of potential models, we perform density-functional
calculations and show that many ice-like configurations exist. In some cases
these are unstable with respect to decay into a bi-layer structure, but we
expect tunneling between such structures to be slow. It is shown that there is
one good candidate for a square crystal, which is a peculiar anti-ferroelectric
arrangement of water molecules.
