  Strongly interacting electron systems can provide insight into quantum
many-body phenomena, such as Mott insulating behavior and spin liquidity,
facilitating semiconductor optimization. The Fermi-Hubbard model is the
prototypical model used to study such systems. Recent research, however, has
shown that the extended Fermi-Hubbard model, which accounts for long-range
interactions, is more accurate, especially for systems far from half-filling.
In this study, we use the extended Fermi-Hubbard model to mathematically
analyze charge transport through a lattice of quantum dots. One-dimensional
chains with spinless electrons and source-drain bias are observed, focusing on
the transition between the ground state and the first excited state. Level
repulsion decreases the expected energy levels of anticrossings as the hopping
onto the chain tends to the hopping within the chain. The distribution of
charge density along the chain is characterized in terms of the hopping,
nuclear, and Coulomb parameters and novel plasmonic behavior is analyzed. Minor
perturbations in electron transport are identified, corresponding to the
one-dimensional nature of the observed systems. This research will lead to a
better understanding of electron behavior in silicon-doped semiconductors, like
the formation of correlation-induced band gaps, and open the door to using the
extended Fermi-Hubbard model as a more accurate alternative to study quantum
many-body systems.
