Coupled Yu-Shiba-Rusinov States Induced by a Many-Body Molecular Spin on a Superconductor

A magnetic impurity on a superconductor induces Yu-Shiba-Rusinov (YSR) bound states, detected by tunneling spectroscopy as long-lived quasiparticle excitations inside the superconducting gap. Coupled YSR states constitute basic elements to engineer artificial superconducting states, but their substrate-mediated interactions are generally weak. In this Letter, we report that intramolecular (Hund’s-like) exchange interactions produce coupled YSR states across a molecular platform. We measured YSR spectra along a magnetic iron-porphyrin on Pb(111) and found evidence of two distinct interaction channels, which invert their particle-hole asymmetry across the molecule. Numerical calculations show that the identical YSR asymmetry pattern of the two channels is caused by two spin-hosting orbitals with opposite potential scattering and coupled strongly. Both channels can be similarly excited by tunneling electrons into each orbital, depicting a new scenario for entangled superconducting bound states using molecular platforms.

Figure 1

(a) STM topography of a FeTPP island showing the moiré pattern. Inset: STM topography of a single bright molecule. The twofold shape reflects the saddle-shape conformation acquired by the porphine core, with two pairs of nonequivalent pyrroles [24]. Scale bar represents 4 Å ($V_S=45\mathrm{mV}$, $I=100\mathrm{pA}$.) (b) STM topography of a bright molecular segment ($V_S=45\mathrm{mV}$, $I=100\mathrm{pA}$). (c) $dI/dV$ spectrum obtained with a superconducting tip taken over the center of a FeTPP molecule, as indicated with the red circle in (a). The bare Pb(111) spectrum is shown in black as a reference ($V_S=4\mathrm{mV}$, $I=100\mathrm{pA}$). (d) $dI/dV$ spectra taken over the center of bright FeTPP molecules along the moiré line in (b). The plots are obtained by numerically deconvolving the tip’s superconducting density of states from $dI/dV$ spectra, as in [22]. Analysis of STM and spectroscopy data was performed with the wsxm [32] and spectrafox [33] software packages.

Figure 2

(a) $dI/dV$ spectroscopy on pyrrole (blue) and iron (red) sites of a FeTPP molecule. YSR peaks appear with a pronounced negative differential conductance characteristic of quasiparticle tunneling via YSR states [48]. Inset: Constant current $dI/dV$ maps at the energy of hole and electron components of the YSR states, respectively. The locations of the $dI/dV$ curves are shown in circles. (b) Stacking plot of point $dI/dV$ along the FeTPP, numerically deconvolved following Ref. [22]. ($V_S=4\mathrm{mV}$, $I=100\mathrm{pA}$.) (c) The ratio between the peak’s amplitudes at each polarity [$A_i(V>0)/A_i(V<0)$] follows the same trend for both YSR excitations.

Figure 3

(a) Simulated tunneling spectral functions for two orbitals with strong Hund’s coupling $J_H=0.3$ [in units of the (half)bandwidth] and with potential scattering $\mathcal{U}$ of opposite sign (model parameters $U_{d,1}=U_{d,2}=3$, ${\epsilon }_{d,1}=-0.25$, and ${\epsilon }_{d,2}=-2.74$, the density of states in the band is $\rho =0.5$ and the BCS gap is $\mathrm{\Delta }={10}^{-3}$). We plot results for the case of both orbitals weakly hybridized with the substrate with matrix elements $V_{1,1}=V_{2,1}$ and $V_{2,2}=-V_{1,2}$, such that $\pi \rho V_{1,1}^2=0.05$ and $\pi \rho V_{2,2}^2=0.035$. The orbitals are coupled with an STM tip via hoping constants $t_1$ and $t_2$. (b) Simulated spatial dependence of the tunneling hopping used in (c) to account for the experimental distribution of $p\text{−}h$ asymmetry. (c) Spectral map of YSR excitations with tunneling hopping in (b).

Figure 4

(a) $dI/dV$ spectroscopy of a bright FeTPP molecule once superconductivity has been quenched on both tip and sample at $B=0.5\mathrm{T}$. Blue and red curves were measured on Fe and pyrrole sites, respectively, as shown in panel (b) ($V_S=15\mathrm{mV}$, $I=1\mathrm{nA}$). (b) Constant-height conductance map obtained at $V_S=100\mu \mathrm{V}$ representing the amplitude distribution of the Kondo resonance. (c) $dI/dV$ spectra of FeTPP molecule with increasing out-of-plane magnetic field ($V_S=15\mathrm{mV}$, $I=300\mathrm{pA}$). (d) Simulated spectra and splitting with magnetic field for the parameter set used in Fig. 3.

Figure 5

Wide-range $dI/dV$ spectra of a bright molecule measured on the locations showed in the inset ($V_S=1.5\mathrm{V}$, $I=3\mathrm{nA}$, $V_{\mathrm{rms}}=2\mathrm{mV}$). Inset: constant-height conductance maps measured at $V_S=-200\mathrm{mV}$ and $V_S=+200\mathrm{mV}$, respectively ($I=200\mathrm{pA}$).