Mesoscopic Fluctuations in Quantum Dots in the Kondo Regime

TL;DR

This paper investigates mesoscopic fluctuations of the Kondo temperature and conductance in quantum dots, using random matrix theory to analyze how these properties vary with different lead configurations and the number of channels.

Contribution

It introduces a theoretical framework to calculate the distribution of Kondo temperature and conductance in quantum dots with chaotic dynamics, highlighting the impact of lead channels.

Findings

Conductance distribution is wide for single-channel leads due to $T_K$ fluctuations.

Increasing channels leads to a gradual self-averaging of conductance.

The Kondo temperature distribution exhibits a logarithmic scale fluctuation.

Abstract

Properties of the Kondo effect in quantum dots depend sensitively on the coupling parameters and so on the realization of the quantum dot -- the Kondo temperature itself becomes a mesoscopic quantity. Assuming chaotic dynamics in the dot, we use random matrix theory to calculate the distribution of both the Kondo temperature and the conductance in the Coulomb blockade regime. We study two experimentally relevant cases: leads with single channels and leads with many channels. In the single-channel case, the distribution of the conductance is very wide as $T_K$ fluctuates on a logarithmic scale. As the number of channels increases, there is a slow crossover to a self-averaging regime.