  Atoms deposited on two-dimensional (2D) electronic materials, such as
graphene, can exhibit unconventional many-body correlations, not accessible in
other settings. All of these are driven by van der Waals forces: between the
atoms themselves and atom-material interactions. For example $^4$He atoms on 2D
materials can potentially form a variety of exotic quantum states of matter,
such as two-dimensional supersolids and superfluids, in addition to solid
phases. For the "most quantum" case of a single helium layer we discuss, from a
theoretical perspective, how the effective low-energy (Bose-Hubbard)
description can take advantage of the extreme sensitivity of this unique system
to the interplay between the atomic (helium) and solid-state (graphene)
components. Due to the extraordinary variety and tunability of 2D electronic
materials, we envisage that a wide range of correlated atomic phases can be
realized under favorable conditions. We also outline exciting possibilities in
the opposite extreme of many atomic layers forming a liquid on top of graphene
-- in this case a so-called "spinodal de-wetting" pattern can form at the
liquid-vapor interface which reflects the presence and electronic properties of
graphene underneath. Such patterns could be manipulated by choosing different
atoms and materials, with potential technological applications.
