Water confined between graphene layers: the case for a square ice

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.