Understanding charge-stability diagrams of dopant arrays in Si

Atomically precise fabrication of dopant arrays in Si provides exciting opportunities to perform quantum simulations, study the dynamics of engineered quantum systems, and develop atomic-scale quantum materials. We describe theoretical simulations done for two-dimensional arrays of dopants in Si implemented with an extended range Fermi-Hubbard model and supported by atomistic modelling of the array states. Simulations are done with and without dopant disorder, as a function of the electron-electron interaction to test the limits of weak and strong interaction. Hund’s rule defines the nature of the charged array ground states for large on-site electron-electron repulsion. Ground states for charged arrays can be highly (quasi) degenerate, providing multiple transport channels. Disorder splits these degeneracies, helping define the charge boundaries in charge-stability diagrams. We consider n x m arrays of different sizes to identify the array states that are probed in transport. Results are used to understand charge-stability diagrams recently obtained for two-dimensional arrays of dopants in Si. Implications for using dopant arrays as a quantum lab on a chip are discussed.