Nonequilibrium Keldysh Formalism for Interacting Leads -- Application to Quantum Dot Transport Driven by Spin Bias

TL;DR

This paper extends the Keldysh nonequilibrium Green's function formalism to include Coulomb interactions between a quantum dot and its leads, revealing enhanced Kondo peaks and novel conductance features under spin bias.

Contribution

The authors develop a generalized formalism for interacting leads in quantum dot systems, enabling analysis of nonequilibrium effects and many-body phenomena like the Kondo effect.

Findings

Interacting leads increase Kondo peak heights in the density of states.

Two Kondo peaks appear in spin differential conductance at specific spin bias and Zeeman splitting.

A conductance plateau emerges due to combined spin bias and Zeeman effects, disappearing with asymmetric interactions.

Abstract

The conductance through a mesoscopic system of interacting electrons coupled to two adjacent leads is conventionally derived via the Keldysh nonequilibrium Green's function technique, in the limit of noninteracting leads [see Y. Meir \emph{et al.}, Phys. Rev. Lett. \textbf{68}, 2512 (1991)]. We extend the standard formalism to cater for a quantum dot system with Coulombic interactions between the quantum dot and the leads. The general current expression is obtained by considering the equation of motion of the time-ordered Green's function of the system. The nonequilibrium effects of the interacting leads are then incorporated by determining the contour-ordered Green's function over the Keldysh loop and applying Langreth's theorem. The dot-lead interactions significantly increase the height of the Kondo peaks in density of states of the quantum dot. This translates into two Kondo peaks in the spin differential conductance when the magnitude of the spin bias equals that of the Zeeman splitting. There also exists a plateau in the charge differential conductance due to the combined effect of spin bias and the Zeeman splitting. The low-bias conductance plateau with sharp edges is also a characteristic of the Kondo effect. The conductance plateau disappears for the case of asymmetric dot-lead interaction.