Novel orientational ordering in a K-doped C$_{60}$ monolayer

Orientational ordering, which originates from broken rotational symmetry, is a central feature of a broad range of materials including liquid crystals, quantum magnets, and some biological systems. By doping C$_{60}$ monolayers with alkali impurities, the symmetry of C$_{60}$ molecules can be broken, opening up the possibility for unique two-dimensional molecular orientational ordering. Here we present a scanning tunneling microscopy/spectroscopy study of K$_{x}$C$_{60}$ monolayers on Au(111), $x\ge $4. We find novel orientational orderings in the C$_{60}$ monolayers at different doping levels, which coincide with strong variations in the monolayer local density of states. This demonstrates the importance of the interplay between Coulomb repulsion, electron-phonon coupling, electronic quadrupolar interactions, and direct orbital overlap in determining the behavior of fullerene nanostructures.