Tuning the Coupling of an Individual Magnetic Impurity to a Superconductor: Quantum Phase Transition and Transport

The exchange scattering at magnetic adsorbates on superconductors gives rise to Yu-Shiba-Rusinov (YSR) bound states. Depending on the strength of the exchange coupling, the magnetic moment perturbs the Cooper pair condensate only weakly, resulting in a free-spin ground state, or binds a quasiparticle in its vicinity, leading to a (partially) screened spin state. Here, we use the flexibility of Fe-porphin (FeP) molecules adsorbed on a Pb(111) surface to reversibly and continuously tune between these distinct ground states. We find that the FeP moment is screened in the pristine adsorption state. Approaching the tip of a scanning tunneling microscope, we exert a sufficiently strong attractive force to tune the molecule through the quantum phase transition into the free-spin state. We ascertain and characterize the transition by investigating the transport processes as function of tip-molecule distance, exciting the YSR states by single-electron tunneling as well as (multiple) Andreev reflections.

Figure 1

(a) Schematic dependence of ground and excited states of a magnetic adatom on a superconducting substrate on exchange coupling strength $J$. At weak coupling, the ground state is a free-spin state, while the excited state has a quasiparticle bound to the adatom. At a critical coupling $J_c$, the roles of ground and excited states reverse. (b) Sketch of the forces acting between tip and molecule vs tip-molecule distance. At large distances, attractive forces pull the molecule away from the surface. At closer distance, repulsive forces push the molecule back towards the surface. (c) STM topography image of a FeP island ($V=-45\mathrm{mV}$, $I=50\mathrm{pA}$) with a molecular model (inset). (d) $dI/dV$ spectra acquired with a Pb tip above bare Pb(111) (black), center (blue), and ligand (red, offset for clarity) of a molecule.

Figure 2

Tip approach above Fe center of a FeP molecule (for more data, see [32]). (a) Junction conductance (in $G_0=2e^2/h$) vs tip offset $\mathrm{\Delta }z$. (b) 2D false-color plot of $dI/dV$ spectra recorded at various tip-sample distances, normalized to their conductances at 5 mV. The spectra were acquired after opening the feedback at $V=5\mathrm{mV}$, $I=200\mathrm{pA}$ and subsequently varying the tip height by an offset $\mathrm{\Delta }z$ (lock-in modulation $V_{\mathrm{rms}}=15\mu \mathrm{V}$). (c) Spectra before ($\mathrm{\Delta }z=-140\mathrm{pm}$, brown trace), at ($\mathrm{\Delta }z=-150\mathrm{pm}$, claret), and after ($\mathrm{\Delta }z=-160\mathrm{pm}$, blue) the quantum phase transition (offset for clarity). (d) Extracted YSR energies and intensity asymmetries vs junction conductance. Error bars determined from peak widths and noise level of the spectra. Around $G=0.02\times G_0$ ($\mathrm{\Delta }z=-150\mathrm{pm}$), the YSR state energy crosses zero and the asymmetry changes sign, indicating the quantum phase transition. (e) Single-electron tunneling processes for YSR resonances at positive and negative bias voltages.

Figure 3

Tip approach above Fe ligand of FeP molecule [see Fig. 1] (for more data see [32]). (a) Evolution of conductance with tip offset $\mathrm{\Delta }z$. (b) 2D false-color plot of $dI/dV$ spectra recorded at various tip-sample distances, normalized to their conductances at 5 mV. (c) Extracted YSR energies and intensity asymmetries vs junction conductance. (d) Four spectra of this approach set (offset for clarity). The YSR state does not reach zero energy and the asymmetry remains positive during most of the approach [see the brown, claret, and blue spectra in (d)]. The asymmetry reverses only around $G=0.1\times G_0$, where Andreev reflections become dominant [see blue and purple spectra in (d)].

Figure 4

(a) Closer view of the approach set in Fig. 3. (b) Four spectra (offset for clarity) of this set showing two peaks due to the Andreev processes depicted in (c). An electron (hole) is reflected through the junction until its energy matches the YSR state. (d) Extracted positions of the peaks shown in (a) and (b) (rectangles) as well as traces showing the expected positions of a thermal excitation of the YSR state (black trace) and of the processes shown in (c) (yellow and pink) given the position of the YSR state.