Electronic transport via localized states in Keldysh non-equilibrium diagram technique

Keldysh non-equilibrium diagram technique is used for a detailed description of electronic transport through a system of localized states. Particular attention is paid to the predictive ability of the theory, for which the number of free parameters in the second-quantized Hamiltonian is reduced. The employed formalism accounts for Coulomb interaction and rigorously treats multi-electron effects and the discreteness of the energy spectra of such structures as induced quantum dots, systems of impurity atoms, or charge centers of metal-organic framework polymers. The proposed algorithm for calculating electric currents and occupation numbers of localized states is implemented in software and tested on a model system with two consecutive two-level quantum dots. The calculated volt-ampere characteristic and current stability diagram are intuitively explained using illustrative energy diagrams. The model successfully reproduces typical single-electron effects: resonant tunneling, negative differential resistance, population inversion in a multilevel system, Coulomb correlations and an indirect manifestation of the memory effect.