Microscopic resolution of the interplay of Kondo screening and superconducting pairing: Mn-phthalocyanine molecules adsorbed on superconducting Pb(111)

Magnetic molecules adsorbed on a superconductor give rise to a local competition of Cooper pair and Kondo singlet formation inducing subgap bound states. For manganese-phthalocyanine molecules on a Pb(111) substrate, scanning tunneling spectroscopy resolves pairs of subgap bound states and two Kondo screening channels. We show in a combined approach of scaling and numerical renormalization group calculations that the intriguing relation between Kondo screening and superconducting pairing is solely determined by the hybridization strength with the substrate. We demonstrate that an effective one-channel Anderson impurity model with a sizable particle-hole asymmetry captures universal and nonuniversal observations in the system quantitatively. The model parameters and disentanglement of the two screening channels are elucidated by scaling arguments.

Figure 1

(a) Molecular structure of manganese-phthalocyanine (MnPc). (b) Constant-current STM image of highly ordered island of MnPc on Pb(111) ($I=23$ pA, $V=100$ mV). (c) Tunneling spectra taken on different molecules on top of the Mn center (feedback opened at $I=450$ pA, $V$ = 8.6 mV). Also shown are the fits used to derive the deconvoluted spectra below in (d). (e) Examples of NRG spectra with broadened subgap peaks for similar $E_{b,\alpha }$.

Figure 2

Ratio of bound state weights $w_{b,g}/w_{b,s}$ vs. bound state energy $E_{b,g}/{\Delta }_{\mathrm{sc}}$. Comparison of experimental results with theory. In all the range of bound state energy we used the model parameters ${\varepsilon }_d/{\Delta }_{\mathrm{sc}}\approx -73$, and $U/{\Delta }_{\mathrm{sc}}\approx 91$ and the overlap $\Gamma$ was varied.

Figure 3

(a) Tunneling spectrum showing the Shiba states (feedback opened at $I=450$ pA, $V$ = 8.6 mV). (b) Tunneling spectrum on the same molecule as in (a) in a larger energy scale evidencing a broad background, which can be fitted by two Kondo resonances (feedback opened at $I=470$ pA, $V$ = 130 mV). (c) Bound state energies $E_{b,\alpha }/{\Delta }_{\mathrm{sc}}$ vs Kondo temperature $T_{\mathrm{K}}/{\Delta }_{\mathrm{sc}}$. Comparison of experimental results with theory for the same choice of model parameters as in Fig. 2.

Figure 4

Left: Schematic plot of the bare band and impurity energy scales and depiction of two scaling regimes (I,II). Right: Schematic plot of the scaling of the effective level ${\varepsilon }_{d,1}$ and ${\varepsilon }_{d,1}+U_1$ in the two regimes $\Lambda \in (D_l,D_u)$ and $\Lambda \in (T_{\mathrm{K},2},D_l)$. Scaling stops at $\Lambda \sim T_{\mathrm{K},2}$, and the effective one-band model is used to compute the low energy properties.