Kondo Impurity in a Mesoscopic Ring: Charge Persistent Current

TL;DR

This paper investigates how a magnetic impurity affects the charge persistent current in a mesoscopic ring, revealing that under certain conditions, the impurity does not influence the charge stiffness.

Contribution

It maps the system onto a Kondo model and provides an exact solution for specific flux conditions using Bethe ansatz, highlighting impurity effects on persistent current.

Findings

Charge stiffness is unaffected by the impurity for spin-independent fluxes.

Exact Bethe ansatz solutions are obtained for special flux conditions.

The model distinguishes between even and odd parity channels in the system.

Abstract

We study the influence of a magnetic impurity or ultrasmall quantum dot on the charge persistent current of a mesoscopic ring. The system consists of electrons in a one-dimensional ring threaded by spin-dependent Aharonov-Bohm/Casher fluxes, coupled via an antiferromagnetic exchange interaction to a localized electron. By passing to a basis of electron states with definite parities, the problem is mapped onto a Kondo model for the even-parity channel plus free electrons in the odd-parity channel. States of opposite parities decouple for values of the flux corresponding to periodic or antiperiodic boundary conditions. For these special cases, the model is solved exactly by a Bethe ansatz, allowing for an exact calculation of the charge persistent current. In particular we show that the charge stiffness in the special case of spin-independent fluxes is insensitive to the presence of the magnetic impurity/quantum dot.