Phase Controlled Superconducting Proximity Effect Probed by Tunneling Spectroscopy

Using a dual-mode STM-AFM microscope operating below 50 mK we measured the local density of states along small normal wires connected at both ends to superconductors with different phases. We observe that a uniform minigap can develop in the whole normal wire and in the superconductors near the interfaces. The minigap depends periodically on the phase difference. The quasiclassical theory of superconductivity applied to a simplified 1D model geometry accounts well for the data.

Figure 1

(a) LDOS in a 1D SNS structure, obtained by solving the Usadel equations of the quasiclassical theory of superconductivity in diffusive metals, taking into account scattering at interfaces and geometrical parameters [15]. $\Delta$ is the gap of the superconductor. A uniform minigap $\delta$, defining a range of energy $2\delta$ in which the LDOS is exactly zero, appears across the normal region and in the S electrodes. In the latter, the finite conductance between $\delta$ and $\Delta$ decreases exponentially away from the interfaces, and the BCS DOS is eventually recovered. The color scale was chosen to enhance the visibility of the minigap. (b) Predicted $2\pi$-periodic phase modulation of $\delta$.

Figure 2

Measured (thick lines) differential conductance taken for zero flux through the loop at various positions (indicated by the arrows and labeled by capital letters) of the four SNS structures shown by the AFM images (taken at 35 mK). The length of the silver wire is, respectively, (a) 300 nm, (b) 500 nm, (c) 900 nm, (d) 2700 nm. The curves are normalized to 1 at large voltage and are shifted by integer numbers for clarity. The thin black solid lines correspond to the model based on the quasiclassical theory of superconductivity introduced in the text and described more in depth in Ref. 15.

Figure 3

Differential conductance $dI/dV(V)$ versus voltage measured in the middle of the 300 nm-long Ag wire (position D) for different values of the phase difference across it as shown by the phase clocks ($\phi /\pi =0.06$, 0.32, 0.57, 0.83; 0.96, 1.00, 1.08; 1.21, 1.34, 1.46, 1.59).

Figure 4

Differential conductance versus voltage, for different values of the phase difference $\phi$ across the 300 nm-long Ag wire. Left quadrants: measured. Right quadrants: calculated. Top: on the N side (position C); Bottom: on the S side, close to the interface (position B: note that the scale is linear up to 0.02 and logarithmic above, to magnify the variation for small subgap conductance). This shows that the minigap is also present on the superconductor side with the same value as on the N side. Dashed lines are guides to the eye.