The spatial range of the Kondo effect: a numerical analysis

TL;DR

This paper introduces a new method to measure the spatial extent of the Kondo effect by analyzing local density of states modifications, providing a quantitative approach that aligns with previous spin-spin correlation results.

Contribution

It is the first study to use local density of states to estimate the Kondo cloud's spatial range, employing advanced numerical techniques for real-space Green function calculations.

Findings

LDOS modifications reflect the Kondo cloud phenomenology

Range of Kondo correlations depends on the Kondo temperature $T_{\rm K}$

Results agree with spin-spin correlation measurements

Abstract

The spatial length of the Kondo screening is still a controversial issue related to Kondo physics. While renormalization group and Bethe Anzats solutions have provided detailed information about the thermodynamics of magnetic impurities, they are insufficient to study the effect on the surrounding electrons, i.e., the spatial range of the correlations created by the Kondo effect between the localized magnetic moment and the conduction electrons. The objective of this work is to present a quantitative way of measuring the extension of these correlations by studying their effect directly on the local density of states (LDOS) at arbitrary distances from the impurity. The numerical techniques used, the Embedded Cluster Approximation, the Finite U Slave Bosons, and Numerical Renormalization Group, calculate the Green functions in real space. With this information, one can calculate how the local density of states away from the impurity is modified by its presence, below and above the Kondo temperature, and then estimate the range of the disturbances in the non-interacting Fermi sea due to the Kondo effect, and how it changes with the Kondo temperature $T_{\rm K}$. The results obtained agree with results obtained through spin-spin correlations, showing that the LDOS captures the phenomenology of the Kondo cloud as well. To the best of our knowledge, it is the first time that the LDOS is used to estimate the extension of the Kondo cloud.