  The recent experimental fabrication of monolayer and few-layer C60 polymers
paves the way for synthesizing two-dimensional cluster-assembled materials.
Compared to atoms with the SO(3) symmetry, clusters as superatoms (e.g., C60)
have an additional rotational degree of freedom, greatly enriching the phase
spaces of superatom-assembled materials. Using first-principles calculations,
we find the energy barriers of cluster rotation in quasi-tetragonal monolayer
C60 structures are rather low (about 10 meV/atom). The small rotational energy
barriers lead to a series of tetragonal C60 polymorphs with energies that are
close to the experimental quasi-tetragonal (expt-qT) phase. Similarly, several
dynamically stable quasi-hexagonal monolayer C60 structures are found to have
energies within 7 meV/atom above the experimental quasi-hexagonal phase. Our
calculations demonstrate photo-excited electron-hole pairs and electrostatic
doping of electrons can effectively modulate the relative energies of
quasi-tetragonal C60 polymorphs. Particularly, the unstable monolayer expt-qT
phase becomes dynamically stable when it is electrostatically doped with
electrons. In contrast, the relative energies between different quasi-hexagonal
polymorphs are insensitive to electrostatic doping of electrons.
