Emergence of Landauer Transport from Quantum Dynamics: A Model Hamiltonian Approach

Abstract: The Landauer expression for computing current-voltage characteristics in nanoscale devices is efficient and widely applicable but not suited to transient phenomena and time dependent currents because it assumes that the charge carrier population attains a time independent dynamic equilibrium as soon as the external voltage is turned on. In this article, we construct a very general expression for a time dependent current in an electrode-molecule-electrode arrangement. Utilizing a model Hamiltonian, we propagate the Schrodinger wave function equation to numerically compute the time dependent population in the individual sub-systems. The current in each electrode (defined in terms of the rate of change of the corresponding population) has two components, one due to the charges originating from the same electrode and the other due to the charges initially residing at the other electrode. We derive an analytical expression for the first component and illustrate that it agrees reasonably with the numerical counterpart at early times. The structural form reveals that the initial occupancy can be factored out of the time dependent segment of the expression. We take this cue to construct a Landauer style formula and demonstrate that the current obtained from this simplified formula overlaps with our most general numerical current only after the charge flow settles into a steady state. Thus, we illustrate the emergence of Landauer transport from a true first-principles quantum dynamics calculation without any prior assumptions. Subsequently, we investigate the ingredients in our model that regulate the onset time scale of this Landauer regime. We compare the performance of our general current expression with the Landauer current for time dependent electronic coupling. Finally, we comment on the applicability of the Landauer formulas to compute hot-electron current arising upon plasmon decoherence.