Probing the Kondo screening cloud via tunneling-current conductance fluctuations

We show that conductance fluctuations or noise in the conductance of a tunneling current into an interacting electron system is dominated by density-density and (or) spin-spin correlations. This allows one to probe two-particle properties (susceptibilities) and collective excitations by standard experimental tunneling methods. We demonstrate this theoretically, using a many-body calculation for the single-adatom Kondo problem. An example of the two-particle correlations around a single magnetic adatom in the Kondo regime, as would be viewed by a scanning tunneling microscope, is given. The spatial dependence of the local spin and charge correlations of the substrate exhibits a clear signature of the Kondo screening cloud.

Figure 1

(Color online) The zero-frequency nonlocal spin (top) and charge (bottom) susceptibilities, for the single-impurity spin-$\frac{1}{2}$ symmetric Anderson model as a function of the distance from the impurity site and for an inverse temperature of ${\left(k_{\text{B}}T\right)}^{-1}=\beta =200$. Here, ${\tilde{\chi }}_{\text{NL}}=\left[\frac{2{\left(\left|{\mathbf{k}}_{\text{F}}\right|\left|\mathbf{r}\right|\right)}^2}{\pi N_{\sigma }\Gamma }\right]{\chi }_{\text{NL}}$. All other parameters are given in Table . (The gray-scale line shade corresponds to different on-site Coulomb interactions $U$, decreasing from dark to light.)

Figure 2

(Color online) The insets show the local spin (top) and charge (bottom) correlations, Eqs. (4a, 4b), for the single-impurity spin-$\frac{1}{2}$ symmetric Anderson model as a function of the distance from the impurity site and for an inverse temperature of ${\left(k_{\text{B}}T\right)}^{-1}=\beta =200$. The envelope of these susceptibilities for fixed $U=1$ and different temperatures $T$, $\beta ={\left(k_{\text{B}}T\right)}^{-1}$, are also shown for each. The horizontal axis has been rescaled by the Kondo length; ${\xi }_{\text{K}}=\hslash v_{\text{F}}/\left(k_{\text{B}}{T}_{\text{K}}\right)$. The deviations for the spin susceptibility at small distances are purely numerical, coming from a high-energy frequency cutoff. Here, $\tilde{\chi }={\left[\frac{2{\left|{\mathbf{k}}_{\text{F}}\right|}^2{\left|\mathbf{r}\right|}^2}{\pi N_{\sigma }\Gamma }\right]}^2\chi$. (In the inset figure, the gray-scale line shade corresponds to different on-site Coulomb interactions $U$, decreasing from dark to light. While the main figure shows the inverse temperature $\beta$ increasing from light (high temperature) to dark (low temperature) in gray scale.)