Electron transport in the four-lead two-impurity Kondo model: Nonequilibrium perturbation theory with almost degenerate levels

TL;DR

This paper develops a method to efficiently compute the nonequilibrium density matrix of a nanostructure with nearly degenerate levels, applied to a two-quantum-dot Kondo system under bias and magnetic field.

Contribution

It introduces an approach for calculating the nondiagonal density matrix in the cotunneling regime, accounting for level mixing effects in nonequilibrium conditions.

Findings

Off-diagonal density matrix terms significantly affect current calculations.

Level mixing becomes prominent with small level splitting and strong lead coupling.

The method captures the impact of magnetic field and bias on transport properties.

Abstract

The eigenstates of an isolated nanostructure may get mixed by the coupling to external leads. This effect is the stronger, the smaller the level splitting on the dot and the larger the broadening induced by the coupling to the leads. We describe how to calculate the nondiagonal density matrix of the nanostructure efficiently in the cotunneling regime. As an example, we consider a system of two quantum dots in the Kondo regime, the two spins coupled by an antiferromagnetic exchange interaction and each dot tunnel coupled to two leads. Calculating the nonequilibrium density matrix and the corresponding current, we demonstrate the importance of the off-diagonal terms in the presence of an applied magnetic field and a finite bias voltage.