Orbital Picture of Yu-Shiba-Rusinov Multiplets

We investigate the nature of Yu-Shiba-Rusinov (YSR) subgap states induced by single manganese (Mn) atoms adsorbed on different surface orientations of superconducting lead (Pb). Depending on the adsorption site, we detect a distinct number and characteristic patterns of YSR states around the Mn atoms. We suggest that the YSR states inherit their properties from the Mn $d$ levels, which are split by the surrounding crystal field. The periodicity of the long-range YSR oscillations allows us to identify a dominant coupling of the $d$ states to the outer Fermi sheet of the two-band superconductor Pb.

Figure 1

(a),(b) $dI/dV$ spectrum of a Mn adatom (black) and of clean Pb(001) (orange). The inset shows a topography of the adatom. Three subgap resonances $\pm \alpha$, $\pm \beta$, and $\pm \gamma$ are marked by arrows. Set point: 300 pA, 5 mV; modulation: $15\mu {\mathrm{V}}_{\mathrm{rms}}$.

Figure 2

(a) Topography of a Mn adatom on Pb(001). Set point: 50 mV (zoom: 5 mV), 150 pA. (b) $dI/dV$ maps of the adatom depicted in (a) at the energy of the subgap resonances $\pm \alpha$, $\pm \beta$, and $\pm \gamma$ (feedback opened in each pixel at 5 mV and 150 pA; modulation: $25\mu {\mathrm{V}}_{\mathrm{rms}}$). The color scale of $\pm \beta$ is stretched to enhance low intensity features (inset shows $\pm \beta$ with linear scale). The center is $\sim 100$ times more intense than the fourfold symmetric lobes. (c) Schematic top view of the adsorption of a Mn adatom in the (001) hollow site. (d) Corresponding crystal field splitting of the $d$ levels.

Figure 3

(a),(b) $dI/dV$ spectra of the same Mn adatom on Pb(111) in the two adsorption sites as indicated in the figure. The shaded areas mark the two BCS coherence peaks [14] and the normal state. The dashed lines indicate the tip gap ($\pm 1.38\mathrm{mV}$). Set point: 100 pA, 5 mV; lock-in modulation: $15\mu {\mathrm{V}}_{\mathrm{rms}}$. The insets show topographies of the adatom in the respective adsorption site ($2.6\times 2.6{\mathrm{nm}}^2$). (c) Deconvolved sample density of states of ${\mathrm{Mn}}_{\mathrm{Pb}(111)}^{\mathrm{down}}$ exhibits five YSR resonances ($\pm \alpha ,\dots ,\pm ϵ$). (d) Deconvolved density of states of ${\mathrm{Mn}}_{\mathrm{Pb}(111)}^{\mathrm{up}}$ shows three YSR resonances ($\pm \zeta$, $\pm \eta$, $\pm \theta$). (e),(f) $dI/dV$ maps of the YSR resonances in both adsorption sites (feedback opened in each pixel at 5 mV and 400 pA; modulation: $20\mu {\mathrm{V}}_{\mathrm{rms}}$). Crosses denote the same position in all maps. The dark spot in the top right corner is a subsurface neon inclusion. The color scale is stretched to give the best contrast to spatially extended features (for maps with linear color scale, see Supplemental Material [24]). (g) Crystal field splitting of the $d$ levels for an adatom in a hollow site.

Figure 4

Lateral evolution of the spectral intensity at positive (black) and negative bias (blue) of the two YSR resonances with lowest binding energy for ${\mathrm{Mn}}_{\mathrm{Pb}(111)}^{\mathrm{up}}$. Set point: 400 pA, 4 mV; modulation: $20\mu \mathrm{V}$. The blue curve is offset by $+1.5$. The $1/r^2$ decay has been removed (for full data see Supplemental Material [24]). The insets show the $dI/dV$ maps at the corresponding energies. The arrows mark the direction along which the intensity is plotted. The $z$ profile gives the apparent height along the distance from the impurity center.