Communication: Relaxation-limited electronic currents in extended reservoir simulations
Daniel S. Gruss, Alexander Y. Smolyanitsky, Michael P. Zwolak
Open system approaches are gaining traction in the simulation of charge transport in nanoscale and molecular electronic devices. In particular, "extended reservoir" simulations, where explicit reservoir degrees of freedom are present, allow for the computation of both real-time and steady state properties but require relaxation of the extended reservoirs. The strength of this relaxation, gamma, influences the conductance, giving rise to a "turnover" behavior analogous to Kramers' turnover in chemical reaction rates. We derive explicit, general expressions for the weak and strong relaxation limits. For weak relaxation, the conductance increases linearly with gamma and every electronic state of the total explicit system contributes to the electronic current according to its "reduced" weight in the two extended reservoir regions. Essentially, this represents two conductors in series -- one at each interface with the implicit reservoirs that provide the relaxation. For strong relaxation, a surprisingly similar expression results, except proportional to 1/gamma. However, it is the reduced weight of the system of interest's electronic states only, reflecting that the strong relaxation is localizing electrons in the extended reservoir regions. Higher order behavior (e.g., gamma^2 or 1/\gamma^2) can occur when there is a gap in the frequency spectrum. We demonstrate these phenomena by examining the current through both simple models and realistic, fluctuating graphene nanoribbons. The expressions for these two regimes allow for benchmarking numerical simulations, as well as illuminate the physical behavior induced by relaxation.