Non-equilibrium electronic transport through a quantum dot with strong Coulomb repulsion in the presence of a magnetic field

Abstract

The non-equilibrium electronic transport through a nanoscale device composed of a single quantum dot between two metallic contacts is studied theoretically within the framework of the Keldysh formalism. The quantum dot consists of a single energy level subject to an applied magnetic field. Correlations due to the Coulomb repulsion between electrons on the dot are treated with a Green's function decoupling scheme which, although similar to the Hubbard-I approximation, captures some of the dynamics beyond. The scheme is exact in the so-called atomic limit, defined by vanishing tunneling between contacts and dot, and in the non-interacting limit, where the on-dot Coulomb repulsion is zero. Explicit analytic solutions, valid for arbitrary magnetic fields, are obtained for two important setups: (i) the stationary regime, with constant voltage bias between the leads, and (ii) the time-dependent regime for metallic leads with constant density of states of infinite width. In these regimes, the current through the dot is evaluated numerically for various parameter sets and its main features interpreted in terms of the underlying physical processes. The results are compared to the non-crossing approximation (NCA) and diagrammatic non-equilibrium quantum Monte-Carlo (QMC) where available.

A many-body approach to transport in quantum systems: from the transient regime to the stationary state

“…Extensions to the single-level quantum devices have included the spin degree of freedom for the study of spin currents, magnetism and torque [57,[442][443][444][445][446][447], establishing that, e.g., tunneling magnetoresistance may transiently develop negative values, and the electronic interactions may enhance this effect. In this regard, the GKBA reconstruction has been shown to capture the essential features of magnetic tunnel currents [448][449][450][451].…”

A many-body approach to transport in quantum systems: From the transient regime to the stationary state

“…Extensions to the single-level quantum devices have included the spin degree of freedom for the study of spin currents, magnetism and torque [57,[398][399][400][401][402][403], establishing that, e.g., tunneling magnetoresistance may transiently develop negative values, and the electronic interactions may enhance this effect. In this regard, the GKBA reconstruction has been shown to capture the essential features of magnetic tunnel currents [404][405][406][407].…”

Nonequilibrium green function technique for analyzing electron transport through single and two levels of interacting quantum dot

“…If the bias window is wider than the separation between the energy levels, two levels lie within the bias widow and two current steps can be obtained. However, the single-level model does not describe this case and another method should be considered to compute the spectra function [21][22][23][24]. The alternative method that can be employed to analyze electron transport through two-level is the equation of motion method.…”

“…independent of energy). Therefore, the expression of spectra function and the transmission function can be given by [21,24]:…”

“…Sierra et al studied the response of electrons transport through two-channel QD to thermal gradients (seebeck effect) that is attributed to the temperature difference of coupled electrodes [23]. The electron transport through Single-level QD with one-site interaction under the effect of the applied magnetic field is analyzed in [24] for time-dependent and time-independent cases. In this paper, the theory of electron transport in nanostructure is presented from the first principle to obtain the Meir-Wingreen formula.…”