Experimental Observation of Bias-Dependent Nonlocal Andreev Reflection

Abstract

We investigate transport through hybrid structures consisting of two normal metal leads connected via tunnel barriers to one common superconducting electrode. We find clear evidence for the occurrence of non-local Andreev reflection and elastic cotunneling through superconductor when the separation of the tunnel barrier is comparable to the superconducting coherence length. The probability of the two processes is energy dependent, with elastic cotunneling dominating at low energy and non-local Andreev reflection at higher energies. The energy scale of the crossover is found to be the Thouless energy of the superconductor, which indicates the phase coherence of the processes. Our results are relevant for the realization of recently proposed entangler devices.

Entangled Andreev pairs and collective excitations in nanoscale superconductors

“…On the other hand, the two processes yield opposite contributions to the non-local conductance (conventionally the CAR contribution is taken as positive) and, as demonstrated by previous theoretical studies 12-14 , tend to cancel each other in the case of Bardeen-Cooper-Schrieffer (BCS) superconductors weakly coupled to non-magnetic leads. Surprisingly, recent experiments by Russo et al 11 have shown that even in this case the subgap non-local conductance can be appreciably large, exhibiting an intriguing behaviour in which either process can dominate depending on the energy of the injected electrons. This behaviour cannot be accounted for by the existing non-interacting theories.…”

“…Within this range of parameters, the lowest energy of the antisymmetric modehω 0 can be of the order of the superconducting gap in Nb, even for the smaller film thickness analysed in ref. 11. To obtain the non-local conductance, G LR , measured at the left interface when a voltage, V , is applied on the right junction, we extend the theory developed for the single mode case, linearizing with respect to the coupling parameters z 1,2 (q) = E c /hω 1,2 (q), which is justified for the range of parameters estimated above.…”

“…In the case of elastic cotunnelling (EC) processes, the injected electron tunnels elastically into the third lead, whereas in the case of crossed Andreev reflection (CAR) processes, it combines with an electron emerging from the third lead to form a Cooper pair in the superconductors. The probability of these processes decays exponentially on the scale of the superconducting coherence length, ξ, which can range between 10 and 100 nm for typical superconductors used in experiments 10,11 . On the other hand, the two processes yield opposite contributions to the non-local conductance (conventionally the CAR contribution is taken as positive) and, as demonstrated by previous theoretical studies 12-14 , tend to cancel each other in the case of Bardeen-Cooper-Schrieffer (BCS) superconductors weakly coupled to non-magnetic leads.…”

High-efficiency Cooper pair splitting demonstrated by two-particle conductance resonance and positive noise cross-correlation

“…Splitting them adiabatically may give birth to entangled electron pairs. Indeed, it had been predicted and measured that Cooper pairs, emanating from a superconductor, can split into two normal metallic leads in the so-called cross Andreev reflection process [4][5][6][7][8][9][10][11] . Such process can be conclusively verified by observing positive coincident arrival events, namely, positive cross-correlation of current fluctuations in two separated normal metallic leads that collect the split pairs [12][13][14][15][16][17][18] .…”

Noise cross-correlation and Cooper pair splitting efficiency in multi-teminal superconductor junctions

“…Our aim is to obtain the noise cross-correlations and the Fano factor. For s-wave superconductors, the nonlocal shot noise has been calculated [32], showing that, whereas the CAR contribute positively to the crossed correlation between the currents in the two leads [48][49][50], the EC contributes negatively [51]. Local processes like the Andreev reflections (AR) and quasiparticles transmission (Q) contribute negatively to the nonlocal shot noise (see Fig.…”