Scanning Tunneling Spectroscopy Study of the Proximity Effect in a Disordered Two-Dimensional Metal

The proximity effect between a superconductor and a highly diffusive two-dimensional metal is revealed in a scanning tunneling spectroscopy experiment. The in situ elaborated samples consist of superconducting single crystalline Pb islands interconnected by a nonsuperconducting atomically thin disordered Pb wetting layer. In the vicinity of each superconducting island the wetting layer acquires specific tunneling characteristics which reflect the interplay between the proximity-induced superconductivity and the inherent electron correlations of this ultimate diffusive two-dimensional metal. The observed spatial evolution of the tunneling spectra is accounted for theoretically by combining the Usadel equations with the theory of dynamical Coulomb blockade; the relevant length and energy scales are extracted and found in agreement with available experimental data.

Figure 1

(a) Topographic constant current ($I=0.1\mathrm{nA}$, $V=25\mathrm{mV}$) STM image: Pb islands (7–13 monolayers high) interconnected by the wetting layer cover single atomic terraces of underlying Si substrate. (b) Schematic representation of the STM or STS experiment with a real example of a color-coded STS tunneling conductance map $dI(V=0,\mathit{r})/dV$ superimposed onto 3D topographic STM image. The colors correspond to the conductance variations from 0 nS (“Low”) to 69 nS (“High”). The fully gaped spectra on the Pb island appear in homogeneous grey (red), the normal wetting layer in black (blue), and the proximity region in white (yellow). The dashed line indicates the position of the flat top edge of the Pb island. (c) Spatial variations of the local $dI(V)/dV$ spectra (the conductance varies from 0 to 100 nS) as a function of the distance from the island edge. The dashed line corresponds to the spectrum taken right at the island edge.

Figure 2

(a) Topographic $5\mathrm{nm}\times 5\mathrm{nm}$ STM image (taken at $I=0.1\mathrm{nA}$, $V=20\mathrm{mV}$) showing the atomic pattern at the top of a Pb island. (b) Topographic $30\mathrm{nm}\times 30\mathrm{nm}$ STM image of the wetting layer. (c) Dotted line: characteristic conductance spectrum measured in the WL away from the Pb island (normalized to unity at STS set point $I=0.4\mathrm{nA}$, $V=5\mathrm{mV}$). The solid line corresponds to the fit obtained using the DCB theory described in the text. (d) Considered equivalent circuit of the experiment (see text for details). (e) The $P(E)$ function used to obtain the fit shown in panel (c).

Figure 3

(a) Evolution of measured local tunneling conductance spectra (normalized to unity at STS set point $I=0.4\mathrm{nA}$, $V=5\mathrm{mV}$) as a function of the distance from the island edge. (b) Computed spectra obtained with the combination of the Usadel model and the DCB theory (see text).