Tuning fulleride electronic structure and molecular ordering via variable layer index

C60 fullerides are uniquely flexible molecular materials that exhibit a rich variety of behaviour, including superconductivity and magnetism in bulk compounds, novel electronic and orientational phases in thin films and quantum transport in a single-C60 transistor. The complexity of fulleride properties stems from the existence of many competing interactions, such as electron-electron correlations, electron-vibration coupling and intermolecular hopping. The exact role of each interaction is controversial owing to the difficulty of experimentally isolating the effects of a single interaction in the intricate fulleride materials. Here, we report a unique level of control of the material properties of K(x)C60 ultrathin films through well-controlled atomic layer indexing and accurate doping concentrations. Using scanning tunnelling microscope techniques, we observe a series of electronic and structural phase transitions as the fullerides evolve from two-dimensional monolayers to quasi-three-dimensional multilayers in the early stages of layer-by-layer growth. These results demonstrate the systematic evolution of fulleride electronic structure and molecular ordering with variable K(x)C60 film layer index, and provide essential information for the development of new molecular structures and devices.