Mapping Itinerant Electrons around Kondo Impurities

We investigate single Fe and Co atoms buried below a Cu(100) surface using low temperature scanning tunneling spectroscopy. By mapping the local density of states of the itinerant electrons at the surface, the Kondo resonance near the Fermi energy is analyzed. Probing bulk impurities in this well-defined scattering geometry allows separating the physics of the Kondo system and the measuring process. The line shape of the Kondo signature shows an oscillatory behavior as a function of depth of the impurity as well as a function of lateral distance. The oscillation period along the different directions reveals that the spectral function of the itinerant electrons is anisotropic.

Figure 1

(a) Scheme of the experiment: the green circle marks the impurity position below the surface and constant current topographies ($2\mathrm{nm}\times 2\mathrm{nm}$, $V=10\mathrm{mV}$, $I=2\mathrm{nA}$) of single Co atoms buried below a Cu(100) surface. (b) Corresponding cross sections (shifted vertically for clarity) of each layer along the $x=[010]$ direction, marked by the arrows in (a).

Figure 2

(a) Spectroscopy of a 3 ML Fe impurity, the corresponding topography ($2.5\mathrm{nm}\times 2.0\mathrm{nm}$, $V=-312\mathrm{mV}$, $I=1.8\mathrm{nA}$) is shown in the inset. A pair of $dI/dV$ spectra taken with the STM tip held over the center (purple curve) of the interference pattern, evaluated at the purple cross and over the nearby bare Cu surface (red curve) evaluated above the undisturbed region of the image (red rectangle). (b) Difference of the differential conductance $\Delta dI/dV=dI/dV-d{I}_0/dV$ (green curve) above the impurity ($dI/dV$) and above the free surface ($d{I}_0/dV$). The solid black curve shows a fit to the $\Delta dI/dV$ data described in the text.

Figure 3

Line-shape variation as a function of the lateral tip position. (a) STM constant current topography of a 7th layer Co impurity ($3\mathrm{nm}\times 3\mathrm{nm}$, $V=-300\mathrm{mV}$, $I=2\mathrm{nA}$) and (b) a 4th monolayer Fe impurity ($2\mathrm{nm}\times 2\mathrm{nm}$, $V=-150\mathrm{mV}$, $I=2\mathrm{nA}$), in which the tip position for the different spectra are depicted. Single spectra, displaced vertically for clarity, for different lateral distances, measured from the center along the [010] direction (c) for the 7 ML Co impurity and (d) for the 4 ML Fe impurity. The solid black curve shows fits to the $\Delta dI/dV$ described in the text. Spatial dependence of the line-shape parameter (LSP) for 7 ML Co (e) and for 4 ML Fe (f). Error bars are obtained by the confidence interval of the nonlinear fit. The dashed lines show a model presented in the text.

Figure 4

Experimentally determined line-shape parameter (LSP) for Co atoms as function of the impurity position $d_n$ below the surface (the corresponding topographies are shown in Fig. 1). Measured $\Delta dI/dV$ (green) and calculated spectra (black) with a tip position fixed at the center of the interference pattern. Inset: The obtained LSP (purple dots) decreases linearly. Error bars are obtained by the confidence interval of the non linear fit.