Friedel oscillations and the Kondo screening cloud

TL;DR

This paper investigates the universal behavior of charge density oscillations caused by a magnetic impurity in a metal, revealing a function that describes these oscillations at all distances related to the Kondo screening cloud.

Contribution

It derives and computes the universal function describing Friedel oscillations in the Kondo effect at all length scales, connecting microscopic theory with observable phenomena.

Findings

Universal function F(r/xi_K) describes charge oscillations at zero temperature.

Analytic expressions for F(r/xi_K) are obtained in both short and long distance limits.

Numerical calculations of F(r/xi_K) across all regimes are presented.

Abstract

We show that the long distance charge density oscillations in a metal induced by a weakly coupled spin-1/2 magnetic impurity exhibiting the Kondo effect are given, at zero temperature, by a universal function F(r/xi_K) where r is the distance from the impurity and xi_K, the Kondo screening cloud size =v_F/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/xi_K) are derived in both limits r much less than xi_K and r much greater than xi_K and F is calculated for all r/xi_K using numerical methods.