Deviations and similarities between landauer's approach and the multi-electronic classical master equation in describing nanoscale transport

In this work, we show that the classical master equation (CME) treatment-with the rates obtained via the Fermi golden rule-and the elastic scattering (ES) approach give the same results for a system composed of two states/one level when considering the approximations of (i) non-interacting limit, i.e., the electronic structure of the N-particle states remains frozen even in the presence of an extra particle, (ii) wide-band limit (WBL) approximation, and (iii) excited states are discarded. Although the predictions of these two approaches 'deviate' from each other when more states and/or levels are considered, under the conditions of strong coupling limit and symmetric contacts both treatments capture the same physics involved in the transport process. For other situations-such as asymmetric coupling and/or weak metal-organic coupling-the predictions of these two theories do not agree with each other. Finally, even considering that in our treatment the electronic structure of the system is described at a tight binding level, the corresponding results clearly show the situations where the similarities and differences between the CME and ES approaches can be identified.

Automated summary

In this study, we demonstrate that the classical master equation (CME) treatment and the elastic scattering (ES) approach yield equivalent results for a system consisting of two states/one level under certain approximations. However, when considering more states and/or levels, the predictions of these two approaches deviate. The CME and ES approaches capture the same physics in the transport process under specific conditions, but their predictions differ in other situations.