Kondo screening cloud and the charge staircase in one-dimensional mesoscopic devices

TL;DR

This paper proposes a method to measure the Kondo screening cloud size in one-dimensional systems by analyzing charge quantization and Coulomb blockade features, revealing universal and interaction-dependent scaling behaviors.

Contribution

It introduces a novel approach to probe the Kondo screening cloud via charge steps and flux dependence in mesoscopic devices, accounting for electron interactions.

Findings

Charge steps are controlled by the Kondo effect when system size is comparable to the screening cloud.

The ratio of Coulomb blockade valley widths is a universal scaling function of xi_K/L.

Electron interactions modify the scaling and flux dependence of charge quantization.

Abstract

We propose that the finite size of the Kondo screening cloud, xi_K, can be probed by measuring the charge quantization in a one-dimensional system coupled to a small quantum dot. When the chemical potential, mu in the system is varied at zero temperature, one should observe charge steps whose locations are at values of mu that are controlled by the Kondo effect when the system size L is comparable to xi_K. We show that, if the standard Kondo model is used, the ratio between the widths of the Coulomb blockade valleys with odd or even number of electrons is a universal scaling function of xi_K/L. If we take into account electron-electron interactions in a single-channel wire, this ratio also depends on the parameters of the effective Luttinger model; in addition, the scaling is weakly violated by a marginal bulk interaction. For the geometry of a quantum dot embedded in a ring, we show that the dependence of the charge steps on a magnetic flux through the ring is controlled by the size of the Kondo screening cloud.