Electron and Cooper-pair transport across a single magnetic molecule explored with a scanning tunneling microscope

A scanning tunneling microscope is used to explore the evolution of electron and Cooper-pair transport across single Mn-phthalocyanine molecules adsorbed on Pb(111) from tunneling to contact ranges. Normal-metal as well as superconducting tips give rise to a gradual transition of the Bardeen-Cooper-Schrieffer energy gap in the tunneling range into a zero-energy resonance close to and at contact. Supporting transport calculations show that in the normal-metal–superconductor junctions this resonance reflects the merging of in-gap Yu-Shiba-Rusinov states as well as the onset of Andreev reflection. For the superconductor-superconductor contacts, the zero-energy resonance is rationalized in terms of a finite Josephson current that is carried by phase-dependent Andreev and Yu-Shiba-Rusinov levels.

Figure 1

(a) STM image of a Pb(111) surface covered with Mn-Pc molecules in the submonolayer coverage range (tunneling current $I=100\text{pA}$, bias voltage $V=100\text{mV}$, size: $50\text{nm}\times 50\text{nm})$. Step edges are decorated with molecular rows. Larger substrate terraces exhibit self-assembled ordered arrays with a nearly square superlattice (see text). (b) STM image of an isolated Mn-Pc molecule on Pb(111) $\left(100\text{pA},-10\text{mV},2.6\text{nm}\times 2.6\text{nm}\right)$. (c) Stick-and-ball model of Mn-Pc. (d) Spectra of $dI/dV$ acquired atop Pb(111) (bottom) and the center of Mn-Pc (top) with a W tip $\left(80\text{pA},-10\text{mV}\right)$. The spectrum of Mn-Pc is offset by $2\text{nS}$. The solid line is a fit of the BCS quasiparticle DOS to the experimental data. (e) Like (d), acquired with a Pb-coated W tip $\left(150\text{pA},10\text{mV}\right)$. The spectrum of Mn-Pc is offset by $20\text{nS}$. The discussion of the spectral features is presented in the text.

Figure 2

Conductance $G$ vs tip displacement $\mathrm{\Delta }z$ acquired atop the Mn-Pc center with a W (a) and a Pb-coated W (b) tip. Stars indicate junction conductances at which $dI/dV$ spectra in (c) and (d) were acquired. $\mathrm{\Delta }z=0\text{pm}$ is defined by $0.1\text{nA},-10\text{mV}$ (W tip), and $10\text{mV}$ (Pb tip). Inset to (b): close-up view of the $G$ evolution for $200\text{pm}\le \mathrm{\Delta }z\le 400\text{pm}$ showing deviations from the exponential behavior and indicating relaxation effects. [(c) and (d)] Spectra of $dI/dV$ acquired atop the Mn-Pc center with a W (c) and Pb-coated W (d) tip with increasing junction conductance (from bottom to top). The structured BCS energy gap observed in tunneling spectra evolves into a broad peak centered at zero bias voltage for both junction types. The solid line in the topmost data set of (c) is a fit of the (broadened) BTK DOS to experimental $dI/dV$ data. The feedback loop was deactivated at (c) $-10$ and (d) $10\text{mV}$ for all spectra. Spectra are normalized by $dI/dV$ at the feedback loop parameters and vertically offset. (e) YSR binding energy ${\varepsilon }_{\text{B}}$ extracted from spectra in (d). (f) Asymmetry $(I_{+}-I_{-})/(I_{+}+I_{-})$ of YSR peak heights extracted from spectra in (d).

Figure 3

(a) Sketch of the experimental geometry showing an STM tip, a deposited Mn-Pc molecule and the superconducting substrate. (b) Sketch of the minimal model employed for the geometry in (a). The tip (green dashed line) and the superconducting substrate (purple) are modeled as semi-infinite linear atomic chains with superconducting order parameters ${\mathrm{\Delta }}_{\text{T}}$ and ${\mathrm{\Delta }}_{\text{S}}$, respectively. Electrons in the tip (substrate) move in a single band with hopping parameter $t_{\text{T}}\left(t_{\text{S}}\right)$ and chemical potential ${\mu }_{\text{T}}\left({\mu }_{\text{S}}\right)$. At the molecule site, a local magnetic exchange interaction, $J$, is introduced. The hopping amplitude $\tau \sqrt{t_{\text{T}}{t}_{\text{S}}}$ controls the tip–molecule–substrate coupling with $0\le \tau \le 1$ the total transparency of the junction.

Figure 4

Calculated $dI/dV$ in the limit of a perfect $\left(\tau =1\right)$ contact (a) and in the tunneling $\left(\tau \ll 1\right)$ range (b), without $\left(J=0\right)$ and with $\left(J\ne 0\right)$ magnetic impurity. Evolution of $dI/dV$ without [(c) and (d)] and with [(e) and (f)] a magnetic impurity as a function of the transparency $\tau$. The data of (a)–(c) and (e) were calculated for the electron-hole symmetric case $\left(\mu =0\right)$ and with negligible broadening of the spectral function $\left(\delta \ll \mathrm{\Delta }\right)$. The data of (d) and (f) were calculated for $\mu \ne 0$ and $\delta =0.1\mathrm{\Delta }$. $dI/dV$ data in (c)–(f) are normalized to their maximum value to clearly see the qualitative changes with increasing transmission (from top to bottom).

Figure 5

Contour plots of the spectral function of an S-S junction depending on the phase difference $\mathrm{\Phi }$ between the superconducting electrodes. (a) $J=0,\tau =1$, evolution of the Andreev bound state, which for $\mathrm{\Phi }=0,2\pi$ is located at the edges of the BCS energy gap and evolves into an in-gap state for $0<\mathrm{\Phi }<2\pi$. (b) $J\ne 0,\tau =1$, occurrence of in-gap YSR states. (c) $J\ne 0,\tau <1$, the YSR branches become decoupled from the continuum of quasiparticle states for not perfectly transparent junctions. (d) $J\ne 0,\tau \ll 1$, the YSR energy is essentially independent of the phase difference for tunneling junctions. (e) and (f) Phase-averaged spectral function, ${\langle A\rangle }_{\mathrm{\Phi }}$, of (c) and (d), respectively. ${\langle A\rangle }_{\mathrm{\Phi }}$ may be interpreted as the average spectral function for an electron that enters into the junction at some arbitrary time.