One-Shot Transport Calculations: A Charge-Conserving Solution.

Transport measurements are a common method of characterizing small systems in chemistry and physics. When interactions are negligible, the current through submicrometer structures can be obtained using the Landauer formula. Meir and Wingreen derived an exact expression for the current in the presence of interactions. This powerful tool requires knowledge of the exact Green's function. Alternatively, self-consistent approximations for the Green's function are frequently sufficient for calculating the current while crucially satisfying all conservation laws. We provide here yet another alternative, circumventing the high computational cost of these methods. We present expressions for the electric and thermal currents in which the lowest-order self-energy is summed to all orders (one-shot approximation). We account for both self-energy and vertex corrections such that current is conserved. Our formulas for the currents capture important features due to interactions and, hence, provide a powerful tool for cases in which the exact solution cannot be found.