Understanding transport in dopant arrays in silicon

The recent development of precision phosphorus donor placement in silicon has stimulated the use of donor arrays for quantum simulation of the extended Hubbard and Su-Schrieffer Heeger models. Transport is used to probe the many-body states of these arrays. We employ exact diagonalization combined with non-equilibrium Green's functions to model transport through 3x3 dopant arrays in Si and extract information about the many-body states in the arrays. We characterize the many-body configurations that contribute to the current, determine current magnitudes for different channels, and visualize how the electron flow circumvents disturbances in the form of array randomness. We find that charge stability diagrams are dominated by current channels corresponding to transport along rows in the 3x3 array, as seen experimentally. This response is robust against effects of disorder. Even if a row is blocked by removal of a middle site, current can flow around the blockade. In addition, we model the time evolution of the many-body state of the array when a spin is injected from the source and extracted into the drain. This provides us with a picture of how spin and charge move through the array, establishing the many-body dynamics that could be seen by experiment.