Fermi Liquid Theory for the Persistent Current Past a Side-Coupled Quantum Dot

TL;DR

This paper develops a Fermi Liquid theory to analytically describe the persistent current in a quantum ring with a side-coupled quantum dot, focusing on weak Kondo couplings and large system sizes, and validates it with numerical results.

Contribution

It introduces a Fermi Liquid framework for analyzing persistent currents in quantum dots coupled to rings, providing analytical predictions and validation against numerical methods.

Findings

Analytical expressions for the first two harmonics of persistent current.

Validation of the Fermi Liquid theory with exact diagonalization results.

Definition of a Wilson ratio linking conductance and persistent current.

Abstract

A Fermi Liquid theory is developed for the persistent current past a side coupled quantum dot yielding analytical predictions for the behavior of the first two harmonics of the persistent current as a function of applied magnetic flux. The quantum dot is assumed weakly coupled to a ring of non-interacting electrons and thus appropriately described as a Kondo impurity. The theory is valid at weak Kondo couplings in the regime where the system size, L, is much larger than the size of the Kondo screening cloud, xi_K. The predictions of the Fermi Liquid theory are compared to exact diagonalization results for the persistent current that lend support to the existence of a regime correctly described by this theory. The finite temperature conductance, at T << T_K is also calculated using Fermi liquid theory allowing the definition of a ``Wilson ratio" relating the conductance and the persistent current.