Nonlocal Correlations in Normal-Metal Superconducting Systems

We examine nonlocal effects between normal-metal gold probes connected by superconducting aluminum. For highly transparent $\mathrm{Au}/\mathrm{Al}$ interfaces, we find nonlocal voltages that obey a spatial and temperature evolution distinct from the nonequilibrium charge imbalance signals usually found in such systems. These voltages are consistent with the predicted effects of crossed Andreev reflection and elastic cotunneling, effects that involve coherent correlations between spatially separated electrons.

Figure 1

Schematic representation of electronic processes that contribute to nonlocal voltages in normal-metal/superconductor structures. (a) In CAR, an electron from one normal-metal lead (1) combines with an electron of opposite spin orientation from the second normal lead (2) to form a Cooper pair in the superconductor. (b) In EC, a electron tunnels from normal lead 1 to normal lead 2 through the effective tunnel barrier represented by the superconducting gap. (c) In CI, a quasiparticle current injected from the normal metal into the superconductor results in nonequilibrium electrochemical potentials ${\mu }_{\mathrm{qp}}$ and ${\mu }_{\mathrm{cp}}$ (for quasiparticles and Cooper pairs, respectively) that relax to the electrochemical potential in the bulk of the superconductor on different length scales. The schematic depicts local CI; a nonlocal CI contribution also exists in regions of the superconductor near the $NS$ interface not in the current path.

Figure 2

(a) Temperature-dependent four-terminal resistance of a $NS$ junction shown in the inset. For the measurement, a small ac current is sent from one Au lead to one Al lead, and the resulting four-terminal resistance is measured with a bridge using a lock-in amplifier with the two remaining leads. The size bar in the inset is 300 nm. (b) Differential resistance $dV/dI$ as a function of the dc current $I$ through the junction measured at 300 mK. $I$ is injected in parallel to the ac current for this measurement.

Figure 3

(a) Scanning electron micrograph of a device with six nonlocal leads, each separated by 210 nm. For the measurements, a current $I$ is sent through the lower Au lead into the superconductor as shown, and the resulting four-terminal nonlocal resistance is measured between the Au leads marked 1–6 and the superconducting lead labeled $V-$. A small ac current is used for the temperature dependence measurements, and a dc current $I$ is injected in parallel to the ac current for the differential resistance measurements. The size bar is $1\mu \mathrm{m}$. (b) Temperature dependence of the nonlocal resistance of the sample in (a) measured using the first four leads. The numbers labeling the curves correspond to the lead numbers in (a).

Figure 4

(a) Nonlocal differential resistance of the device in Fig. 3a at 20 mK. The numbers refer to the Au probes in Fig. 3a with which the signal was measured. Inset: Expanded view of the low current-bias regime, showing that the zero-bias differential resistance decays rapidly as one moves away from the $NS$ interface through which the current flows. (b) Zero-bias ($I=0$) resistance (circles) and finite-bias resistance peak (triangles) from (a) as a function of the distance $L$ of the nonlocal probe from the current-carrying $NS$ interface.