Fermi liquid theory for the nonequilibrium Kondo effect at low bias voltages

TL;DR

This paper develops a Fermi liquid theory for the nonequilibrium Kondo effect in quantum dots under finite bias, deriving exact low-energy conductance behavior and providing an alternative quasiparticle-based description.

Contribution

It introduces a nonequilibrium Fermi liquid framework for the Kondo effect, deriving Ward identities and low-energy conductance formulas using microscopic and renormalized perturbation theories.

Findings

Exact low-energy differential conductance up to order (eV)^2

Green's function depends on nonequilibrium distribution f_eff()

Extension of RPT to high-bias regimes beyond Fermi-liquid behavior

Abstract

In this report, we describe a recent development in a Fermi liquid theory for the Kondo effect in quantum dots under a finite bias voltage $V$. Applying the microscopic theory of Yamada and Yosida to a nonequilibrium steady state, we derive the Ward identities for the Keldysh Green's function, and determine the low-energy behavior of the differential conductance $dI/dV$ exactly up to terms of order $(eV)^2$ for the symmetric Anderson model. These results are deduced from the fact that the Green's function at the impurity site is a functional of a nonequilibrium distribution $f_{\text{eff}}(\omega)$, which at $eV=0$ coincides with the Fermi function. Furthermore, we provide an alternative description of the low-energy properties using a renormalized perturbation theory (RPT). In the nonequilibrium state the unperturbed part of the RPT is determined by the renormalized free quasiparticles, the distribution function of which is given by $f_{\text{eff}}(\omega)$. The residual interaction between the quasiparticles $\widetilde{U}$, which is defined by the full vertex part at zero frequencies, is taken into account by an expansion in the power series of $\widetilde{U}$. We also discuss the application of the RPT to a high-bias region beyond the Fermi-liquid regime.