Devloping atom-based solid-state quantum simulators: understanding charge-stability diagrams of dopant arrays in Si

Atomically precise fabrication of dopant arrays in Si provides exciting opportunities to perform quantum simulations and to study the dynamics of engineered quantum systems. Here we describe theoretical simulations done for two-dimensional arrays of dopants in Si used to implement an extended range Fermi-Hubbard model. Simulations are done with and without atom disorder, as a function of the electron-electron interaction to test the limits of weak and strong interaction, and with and without a spin/valley degree of freedom. Results are used to understand charge-stability diagrams, recently obtained for two-dimensional arrays of dopants in Si. The nature of transport through these arrays depends critically on the ratio of the inter-dopant tunneling to tunnel coupling of the dopants to the source and drain. We consider n x m arrays of different sizes to identify the array states that are probed in transport. We further consider the effect of array orientation relative to the source and drain on the tunnel coupling and on the capacitive coupling to side gates. Implications for using dopant arrays as a quantum lab on a chip are discussed.