Proximity Effect between Two Superconductors Spatially Resolved by Scanning Tunneling Spectroscopy

We present a combined experimental and theoretical study of the proximity effect in an atomic-scale controlled junction between two different superconductors. Elaborated on a Si(111) surface, the junction comprises a Pb nanocrystal with an energy gap ${\mathrm{\Delta }}_1=1.2\mathrm{meV}$, connected to a crystalline atomic monolayer of lead with ${\mathrm{\Delta }}_2=0.23\mathrm{meV}$. Using in situ scanning tunneling spectroscopy, we probe the local density of states of this hybrid system both in space and in energy, at temperatures below and above the critical temperature of the superconducting monolayer. Direct and inverse proximity effects are revealed with high resolution. Our observations are precisely explained with the help of a self-consistent solution of the Usadel equations. In particular, our results demonstrate that in the vicinity of the Pb islands, the Pb monolayer locally develops a finite proximity-induced superconducting order parameter, well above its own bulk critical temperature. This leads to a giant proximity effect where the superconducting correlations penetrate inside the monolayer a distance much larger than in a nonsuperconducting metal.

Popular Summary

When a metal and a superconductor are interfaced through a good electrical contact, the electronic properties of the metal in the vicinity of the interface are altered. This phenomenon, known as the proximity effect, has been investigated since the early 1960s. What happens when the two materials in electrical contact are both superconductors and the scale of the contact is atomic? This question takes on renewed importance and interest, because of its relevance to a great variety of hybrid electronic systems based on novel low-dimensional or small-scale materials, as well as the much greater technical possibilities of studying such systems. So far, however, experimental studies that address this question have been scarce. In this paper, we report the first demonstration of a proximity effect between two superconductors connected through an atomic-scale junction, which is resolved in real space experimentally by a very-low-temperature scanning tunneling microscope and quantitatively explained theoretically.

The two superconductors in our system are a submicrometer island of single-crystal Pb and a crystalline monolayer Pb, with the former embedded in the latter. The electrical contact is provided by the atoms on the periphery of the island. Although both can be superconducting, the island becomes so at a much higher temperature than the monolayer, leaving a window of temperature within which the former is already superconducting and the latter still behaves like a normal metal. The density of electronic states in the vicinity of the interface, which we have mapped out with unprecedented 1-nm spatial and 30-meV energy resolutions, reveals a spectacular proximity effect in this temperature range: The region of induced superconductivity in the still metal-like Pb monolayer is many times bigger than what is typically seen in a normal nonsuperconducting metal. All our experimental observations have been given quantitative explanations.

Our conclusions are applicable to a wide range of superconducting heterojunctions. The combination of the experimental technique and the theory paves the way for studying new aspects of the broad concept of the proximity effect, such as the Meissner effect in proximity-induced superconductors.

Figure 1

(a) Topographical STM image of a 7-ML-high Pb island, denoted as $S_1$, surrounded by the SIC Pb monolayer, denoted as $S_2$. Small Pb clusters of few-nanometers size and 1-ML height are visible on the SIC monolayer. These very small clusters result from the extra Pb atoms deposited on the surface in order to form few large islands such as $S_1$. (b) Topographical STM image showing a smaller-scale region representing the atomic superstructure of the SIC monolayer observed everywhere on the surface between the Pb clusters. The images were taken at $V_{\text{bias}}=-1.0\mathrm{V}$ and $I=35\mathrm{pA}$.

Figure 2

$S_1\text{−}{S}_2$ proximity effect at 0.3 K. (a) Topographic STM image of the sample showing the Pb nanoisland $S_1$ connected to the striped incommensurate Pb monolayer $S_2$. The superposed color-coded spectroscopy map at $V_{\text{bias}}=-0.2\mathrm{mV}$ allows one to visualize the proximity effect. The $256\times 256$ spectra were measured in the STS map. (b) Spatial and energy evolution of the experimental tunneling conductance spectra, $dI/dV(V,x)$, across the junction (3 D view). One spectrum is plotted every 1 nm and highlighted by a black line every 10 nm. (c) Color-coded experimental $dI/dV(V,x)$ spectra across the interface. One spectrum is plotted every nanometer. (d) Selected local tunneling spectra (dots). The last spectrum measured on the top flat part of the island before the edge is denoted by $-0\mathrm{nm}$. The first spectrum measured on the SIC monolayer is denoted by $+0\mathrm{nm}$. The distance between the $+0\text{−}\mathrm{nm}$ and $-0\text{−}\mathrm{nm}$ spectra is about 1 nm. (e) Color-coded computed $dI/dV(V,x)$ across the interface. (f) Spatial evolution of the energy of the peak maximum $E_{\text{peak}}(x)$ across the interface. The experimental results (symbols) are nicely reproduced by self-consistent calculation of the order parameter (red solid line), while the red dashed line corresponds to the non-self-consistent result. The evolution of the order parameter is shown by black lines: self-consistent (solid) and non-self-consistent (dashed).

Figure 3

The same as in Fig. 3, but for $T=2.05\mathrm{K}$. At this temperature, the striped incommensurate Pb monolayer $S_2$ is in its normal state. Notice that the order parameter determined self-consistently exhibits a finite value close to the $S_1\text{−}{S}_2$ interface.

Figure 4

The main panel shows the computed order parameter in the Pb monolayer as a function of the distance to the island edge for different temperatures. The critical temperature of the monolayer is, within BCS theory, $T_{C2}=1.51\mathrm{K}$, while it is $T_{C1}=7.89\mathrm{K}$ for the island. The different parameters are those of Fig. 2, and the temperature dependence of ${\mathrm{\Delta }}_1$ has been taken into account. The inset shows the temperature dependence of the decay length $L_{\mathrm{\Delta }}$ of the induced order parameter for temperatures above $T_{C2}$ (see text for a definition). The symbols correspond to the values extracted from the curves shown in the main panel, while the red solid line is a numerical fit of those results to a function of around $1/\sqrt{T-T_{C2}}$.

Figure 5

Inverse proximity effect in the $S_1$ island at 0.3 K, and color-coded experimental $dI/dV(V,x)$ spectra across the $S_1\text{−}{S}_2$ junction. One spectrum is plotted every nanometer. The four-decade log color scale allows one to visualize two important effects as one approaches the $S_1\text{−}{S}_2$ interface: (i) reduction of the peak energy and amplitude (pink narrow $dI/dV>1$ band) and (ii) appearance of a tail of induced subgap states in the region ${\mathrm{\Delta }}_2\le e{V}_{\text{bias}}\le {\mathrm{\Delta }}_1$.

Figure 6

Determination of the zero-temperature bulk gaps. (a) Normalized tunneling spectra as a function of the bias voltage. The symbols correspond to the experimental spectrum measured at 0.3 K deep inside the Pb island ($x=-80\mathrm{nm}$). The solid line corresponds to the best fit obtained with the BCS theory for ${\mathrm{\Delta }}_1=1.2\mathrm{meV}$ and $T=0.55\mathrm{K}$. (b) The same as in the upper panel but for a spectrum measured in the Pb monolayer very far away from the island edge ($x=+200\mathrm{nm}$). The BCS tunneling spectrum was obtained using ${\mathrm{\Delta }}_2=0.23\mathrm{meV}$ and $T=0.55\mathrm{K}$.

Figure 7

The lower panels show the computed normalized $dI/dV$ as a function of the bias voltage for $T=0.55\mathrm{K}$ and $r=0.0$ (perfect transparency). The different curves correspond to different positions along the monolayer, $x$. The curves were computed in steps of 10 nm ranging from $x=0$ (island edge) to $x=100\mathrm{nm}$. The lower left panel corresponds to a calculation where the order parameter in the monolayer is assumed to be constant and equal to its bulk value. The lower right panel corresponds to the case in which the order parameter has been calculated in a self-consistent manner. The upper panels show the corresponding order-parameter profiles.

Figure 8

The same as in Fig. 7, but for $T=2.05\mathrm{K}$. At this temperature, the monolayer is in its normal state. Notice that the order parameter determined self-consistently exhibits a finite value in the vicinity of the island.

Figure 9

Normalized tunneling conductance at $T=0.55$ K as a function of the bias voltage for different values of the interface parameter $r$, as indicated in the panels. The different curves correspond to different positions along the monolayer, $x$. The curves were computed in steps of 10 nm ranging from $x=0$ (island edge) to $x=100\mathrm{nm}$. The black dashed lines in the different panels correspond to the spectra inside the island, while the black solid lines are the results obtained on the monolayer side of the island edge. Notice the discontinuity in the spectra at the island edge when $r\ne 0$.

Figure 10

The same as in Fig. 9, but for $T=2.05\mathrm{K}$.

Figure 11

Self-consistent order parameter as a function of the position for different values of $r$ and for temperatures (a) $T=0.55\mathrm{K}$ and (b) $T=2.05\mathrm{K}$. These profiles correspond to the cases shown in Figs. 9 and 10.

Figure 12

Computed normalized tunneling spectra as a function of the bias and the position measured with respect to the island edge. (a) Results obtained in a self-consistent calculation using the following parameter values: $T=2.05\mathrm{K}$, ${\mathrm{\Delta }}_1=1.2\mathrm{meV}$, ${\mathrm{\Delta }}_2=0.23\mathrm{meV}$, $r=0.02$, and $D_2=7.3{\mathrm{cm}}^2/\mathrm{s}$. (b) The same as in panel (a) but for a non-self-consistent calculation where the order parameter is assumed to vanish in the monolayer.

Figure 13

The lower panels show the computed normalized density of states as a function of energy (measured with respect to the Fermi energy, $E_{\text{F}}$). The parameters of the model are those of Fig. 12, and the different curves correspond to different positions along the monolayer, $x$. The curves were computed in steps of 10 nm, ranging from $x=0$ (monolayer side of the island edge) to $x=100$ nm. The lower left panel corresponds to a calculation where the order parameter in the monolayer is assumed to be zero everywhere, while the lower right panel corresponds to the case in which the order parameter was calculated in a self-consistent manner. The upper panels show the corresponding order-parameter profiles (black lines) and the spatial evolution of the coherent peaks (red lines).

Figure 14

Normalized tunneling spectra as a function of the bias voltage and the position measured with respect to the island edge. These results were obtained in self-consistent calculations that take into account the inverse proximity effect in the island. The three panels correspond to different values of the diffusion constant ratio $r_{\text{diff}}=D_1/D_2$. The different parameter values are $T=0.55\mathrm{K}$, ${\mathrm{\Delta }}_1=1.2\mathrm{meV}$, ${\mathrm{\Delta }}_2=0.23\mathrm{meV}$, $r=0.0$, and $D_2=7.3{\mathrm{cm}}^2/\mathrm{s}$.