Kondo effect in complex mesoscopic structures

TL;DR

This paper analytically investigates the Kondo effect in complex mesoscopic structures with a quantum dot, deriving explicit Green function expressions that incorporate structure effects through self-energy, and validating them on specific models.

Contribution

It introduces an explicit analytic approximation for the quantum dot Green function in complex structures, considering strong interactions and Fermi-liquid relations.

Findings

The derived Green function satisfies Fermi-liquid relations at zero temperature.

The expression effectively captures the influence of complex structures via self-energy.

Validation on the Anderson model and T-shaped network confirms its applicability.

Abstract

We study the Kondo effect of a quantum dot placed in a complex mesoscopic structure. Assuming that electronic interactions are taking place solely on the dot, and focusing on the infinite Hubbard interaction limit, we use a decoupling scheme to obtain an explicit analytic approximate expression for the dot Green function, which fulfills certain Fermi-liquid relations at zero temperature. The details of the complex structure enter into this expression only via the self-energy for the non-interacting case. The effectiveness of the expression is demonstrated for the single impurity Anderson model and for the T-shaped network.