Friedel oscillations and the Kondo screening cloud

Abstract

We show that the long-distance charge-density oscillations in a metal induced by a weakly coupled spin-$\frac{1}{2}$ magnetic impurity exhibiting the Kondo effect are given, at zero temperature, by a universal function $F(r∕{\ensuremath{\xi}}_{K})$, where $r$ is the distance from the impurity and ${\ensuremath{\xi}}_{K}$ is the Kondo screening cloud size $\ensuremath{\equiv}\ensuremath{\hbar}{v}_{F}∕({k}_{B}{T}_{K})$, where ${v}_{F}$ is the Fermi velocity and ${T}_{K}$ is the Kondo temperature. $F$ is given by a Fourier-like transform of the $T$ matrix. Analytic expressions for $F(r∕{\ensuremath{\xi}}_{K})$ are derived in both limits $r⪡{\ensuremath{\xi}}_{K}$ and $r⪢{\ensuremath{\xi}}_{K}$ and $F$ is calculated for all $r∕{\ensuremath{\xi}}_{K}$ using numerical methods.