# Observation of the Kondo Screening Cloud of Micron Lengths

## TL;DR

This paper provides experimental evidence of the Kondo screening cloud extending over micrometers, confirming a fundamental aspect of the Kondo effect and demonstrating a new method to detect spatial spin correlations.

## Contribution

The study experimentally observes the Kondo cloud over micron lengths using electron interferometry, confirming the theoretical length scale $\xi_ ext{K}$ and its role in the Kondo effect.

## Key findings

- Kondo cloud extends over micrometers, comparable to $\xi_ ext{K}$
- Oscillations in $T_ ext{K}$ depend on the length $L$ and scale with $L/\xi_ ext{K}$
- The Kondo length $\xi_ ext{K}$ is the key spatial parameter of the effect

## Abstract

When a magnetic impurity exists in a metal, conduction electrons form a spin cloud that screens the impurity spin. This basic phenomenon is called the Kondo effect. Contrary to electric charge screening, the spin screening cloud occurs quantum coherently, forming spin-singlet entanglement with the impurity. Although the spins interact locally around the impurity, the cloud can spread out over micrometers. The Kondo cloud has never been detected to date, and its existence, a fundamental aspect of the Kondo effect, remains as a long-standing controversial issue. Here we present experimental evidence of a Kondo cloud extending over a length of micrometers comparable to the theoretical length $\xi_\mathrm{K}$. In our device, a Kondo impurity is formed in a quantum dot (QD), one-sided coupling to a quasi-one dimensional channel~\cite{Theory_Proposal_HS} that houses a Fabry-Perot (FP) interferometer of various gate-defined lengths $L > 1 \, \mu$m. When we sweep a voltage on the interferometer end gate separated from the QD by the length $L$ to induce FP oscillations in conductance, we observe oscillations in measured Kondo temperature $T_\mathrm{K}$, a sign of the cloud at distance $L$. For $L \lesssim \xi_\mathrm{K}$ the $T_\mathrm{K}$ oscillation amplitude becomes larger for the smaller $L$, obeying a scaling function of a single parameter $L/ \xi_\mathrm{K}$, while for $L>\xi_\mathrm{K}$ the oscillation is much weaker. The result reveals that $\xi_\mathrm{K}$ is the only length parameter associated with the Kondo effect, and that the cloud lies mostly inside the length $\xi_\mathrm{K}$ which reaches microns. Our experimental method of using electron interferometers offers a way of detecting the spatial distribution of exotic non-Fermi liquids formed by multiple magnetic impurities or multiple screening channels and solving long-standing issues of spin-correlated systems.