New study of shot noise with the nonequilibrium Kubo formula in mesoscopic systems, application to the Kondo effect at a quantum dot

TL;DR

This paper introduces a nonequilibrium Kubo formula for shot noise in mesoscopic systems, applying it to the Kondo effect in quantum dots, revealing universal behavior of the Fano factor related to the Wilson ratio.

Contribution

It develops a new theoretical approach using the nonequilibrium Kubo formula to analyze shot noise in correlated mesoscopic systems at any temperature and bias.

Findings

Fano factor in the Kondo regime is universal and depends on the Wilson ratio.

At R=2, the Fano factor equals 5/3, matching previous results.

The approach confirms shot noise equals the zero-temperature noise power in leading order.

Abstract

Recently we have developed a theory of Keldysh formalism for mesoscopic systems. The resulting nonequilibrium Kubo formula for differential conductance makes it possible to propose the new formula of shot noise $S_h$, and thus to study shot noise in correlated systems at any temperature and any bias voltage. Employing this new approach, we analyze shot noise in the Kondo regime through a quantum dot for the symmetric case at zero temperature. Using the renormalized perturbation theory, we prove that in the leading order of bias voltage $S_h$ equal to noise power at zero temperature conventionally used as shot noise. With $S_h$, we calculate the Fano factor for a backscattering current $I_b$: $F_b=S_h/2eI_b$. It is shown that the Fano factor takes the universal form of $F_b=1+4(R-1)^2/(1+5(R-1)^2)$ determined by the Wilson ratio $R$ for arbitrary strength of the Coulomb interaction. Using the Wilson ratio R=2, our result coincides with the fractional value of $F_b=5/3$ already derived in the Kondo regime.