Simulation of Transport through semiconductor arrays using the extended reservoir approach

Recent breakthroughs in nanoscale device fabrication in semiconductors has allowed the precision placement of phosphorus (P) dopants in bulk silicon (Si) to create locally confined donor arrays as device platforms forin analog quantum simulations. This calls for accurate simulations of the dynamics of transport through such arrays when they are electronically coupled to a source and a drain. Traditional methods such as exact diagonalization are not capable of simulating the reservoir beyond a few atomic sites, and a naïve application of tensor network techniques might suffer from a rapid growth of entanglement between the leads. Here we employ the extended reservoir approach to study such systems, where the source and drain are modeled as discrete energy modes that are directly coupled to the array sites. This minimizes the entanglement generation at the lead interfaces and allows for more effective simulations at longer time scales. We investigate the impact of varying the simulation parameters, including the source and drain couplings, potential biases across different parts of the system, and strength of many-body interactions within the arrays and the reservoirs. We observe distinctively different transport dynamics across several regimes. Lastly we explore the possibility of applying these techniques to studying the dynamics in the Nagaoka Ferromagnetism.