Experiments on nonlocal processes in NS devices

In this thesis we have used the angle-evaporation technique to prepare multi-terminal normal metal-insulator-superconductor (NIS) hybrid devices with minimum contact distances of ~50nm. On these samples we performed local measurements for junction characterizations and nonlocal measurements to study crossed Andreev reflection (CAR), elastic cotunneling (EC) and nonlocal charge imbalance (CI).
In nonlocal measurements we found that spurious effects like capacitive cross-talk, leakage currents or inhomogeneous currents paths can cause nonlocal signals in the detector possibly resembling expected nonlocal characteristics. Thus, we introduced criteria and control measurements for trustworthy nonlocal results.
For the detection of nonlocal processes we measured the nonlocal resistance R_{nl} as a function of bias, temperature T and applied magnetic field H. In our results we distinguished the competing nonlocal processes, namely crossed Andreev reflection, elastic cotunneling and nonlocal charge imbalance, by their sign of R_{nl} and by their T-dependence.
We find that in a small window of contact resistances CAR dominates the nonlocal subgap transport. This window is small as in the lower limit, namely in high-transparent samples, EC and CI dominate the transport at subgap energies as confirmed by theory and experiments. Our results give the upper limit as they show that in low-transparent devices with resistance area products (RA) approximately larger than 100\Omega\mu*m^2 EC dominates around zero bias.
Based on these findings we studied the contact resistance dependence of CAR on three different samples and find a successive change of the midgap R_{nl} characteristics with increasing injector and detector contact resistance. Our results show that for low resistance area products and low temperatures T<0.5K CAR can dominate the nonlocal transport for all subgap biases, whereas for higher T and for bias potentials larger than the superconducting energy gap nonlocal CI dominates. With increasing resistance area product CAR weakens and EC becomes prominent around zero bias. The contact resistance dependence of the subgap transport can qualitatively be understood based on charging effects on the small contact capacitances known as dynamical Coulomb blockade (DCB). However, the origin of the CAR dominance at low RA (~10-20\Omega\mu*m^2) remains unclear.
For a further understanding of the interplay between the competing nonlocal processes, we investigated their dependence of a magnetic field applied in-plane of the device. For H<<H_{C} CAR and EC are independent of the magnetic field. Close to the critical magnetic field H_{C} where the superconducting gap is strongly reduced, CI starts to dominate. CI, however, is already suppressed for low magnetic fields due to orbital pair breaking. We fit the CI results to the local CI theory and extract an inelastic quasiparticle relaxation time of 0.25ns, considerably smaller as reported for thick and thin films, but in agreement with CI lengths obtained in recent experiments on superconducting Al wires in other groups. We attribute the reduced relaxation time to an enhanced electron-electron scattering. In contrast to CI, CAR is independent of H for low fields, which opens a novel possibility to distinguish these processes.
As we have studied the contact resistance dependence of CAR and EC, the same is necessary for nonlocal CI since a deeper understanding allows a better control over these processes. We find that for bias potentials larger than the superconducting energy gap the nonlocal resistance and thus nonlocal CI is determined by the injector and not the detector. This is in contrast to the ``standard'' theory of CI most likely due to an appreciable supercurrent flowing in the device in this bias regime. For subgap energies, however, different injector-detector pairs exhibit within noise similar nonlocal resistances. With a recently published theoretical model it was possible to reproduce quantitatively this very weak dependence of nonlocal CI on the injecting and detecting contact resistance. In collaboration with D. Golubev and A. Zaikin we adapted this model in such a way that it only incorporates experimentally accessible parameters.
To sum up, this thesis has studied the interplay between crossed Andreev reflection, elastic cotunneling and nonlocal charge imbalance and has most importantly demonstrated the dependence of crossed Andreev reflection on the contact resistance. This is an important finding as it gives a potential control on the nonlocal processes which is of high interest for the development of a solid-state entangler.