Nonequilibrium Diagram Technique Applied to the Electronic Transport via Tightly Bound Localized States

Abstract

Keldysh nonequilibrium diagram technique is used for a detailed description of electron transport through a system of tightly bound spatially separated localized states. Particular attention is paid to the predictive ability of the effective theory, for which the number of free parameters in the second-quantized Hamiltonian is reduced. The employed formalism in a variant of tight-binding model rigorously treats multi-electron tunneling effects and the discreteness of the energy spectra in low-dimensional structures. The model is also extended with Coulomb interaction of moderate strength. Proposed algorithm for calculating electric currents and occupation numbers of localized states in presence of weak Coulomb repulsion is implemented in software and tested on a model system of two consecutive three-level quantum dots. Electron transfer proceeds both sequentially between the dots and in parallel within each quantum dot. The calculated IV-curve and current stability diagram are intuitively explained using coordination energy diagrams. The model qualitatively reproduces typical effects in interference-based nanoelectronics: resonant tunneling, negative differential resistance, population inversion in a multi-level system. The impact of moderate Coulomb correlations on current stability diagram is examined. This demonstrates the capability of extended tight-binding model to incorporate weak Coulomb interaction into the description of electronic transport via discrete quantum states.