No abstract

Ferromagnetism is usually considered to be incompatible with conventional superconductivity, as it destroys the singlet correlations responsible for the pairing interaction. Superconductivity and ferromagnetism are known to coexist in only a few bulk rare-earth materials. Here we report evidence for their coexistence in a two-dimensional system: the interface between two bulk insulators, LaAlO(3) (LAO) and SrTiO(3) (STO), a system that has been studied intensively recently. Magnetoresistance, Hall, and electric-field dependence measurements suggest that there are two distinct bands of charge carriers that contribute to the interface conductivity. The sensitivity of properties of the interface to an electric field makes this a fascinating system for the study of the interplay between superconductivity and magnetism.

We examine nonlocal effects between normal-metal gold probes connected by superconducting aluminum. For highly transparent Au/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.

We report measurements of the thermopower S of mesoscopic Andreev interferometers, which are hybrid loops with one arm fabricated from a superconductor (Al), and one arm from a normal metal (Au). S depends on the phase of electrons in the interferometer, oscillating as a function of magnetic flux with a period of one flux quantum (= h/2e). The magnitude of S increases as the temperature T is lowered, reaching a maximum around T = 0.14 K, and decreases at lower temperatures. The symmetry of S oscillations with respect to magnetic flux depends on the topology of the sample.Comment: 4 pages, 4 figure

Non-local entanglement is a key ingredient to quantum information processing. For photons, entanglement has been demonstrated 1 , but it is more difficult to observe for electrons. One approach is to use a superconductor, where electrons form spin-entangled Cooper pairs, which is a natural source for entangled electrons. For a three-terminal device consisting of a superconductor sandwiched between two normal metals, it has been predicted that Cooper pairs can split into spinentangled electrons flowing in the two spatially separated normal metals 2-5 , resulting in a negative non-local resistance and a positive current-current correlation 6,7 . The former prosperity has been observed 8,9 , but not the latter. Here we show that both characteristics can be observed, consistent with Cooper-pair splitting. Moreover, the splitting efficiency can be tuned by independently controlling the energy of the electrons passing the two superconductor/normal-metal interfaces, which may lead to better understanding and control of non-local entanglement.Entanglement of electrons may arise in the spatial degree of freedom (orbital entanglement) or the spin degree of freedom (spin entanglement). Recently, orbital entanglement in a fermionic Hanbury Brown and Twiss two-particle interferometer was observed using current cross-correlation measurements 10,11 , but further investigation is still required to verify the entangled states 12 . Spin-entanglement has been predicted to exist at the superconductor/normal-metal (SN) interface 2,3 and can be understood in the context of Andreev reflection 13 , in which a low-energy electron in the normal metal impinges on the SN interface and a hole is retroreflected whereas a Cooper pair is created in the superconductor.When two normal metals are coupled to a superconductor with spatial separation comparable to the superconducting coherence length (ξ S ), roughly the size of a Cooper pair, it is predicted that electrons in the two normal metals can also be coupled by means of a non-local analogue of Andreev reflection called crossed Andreev reflection 6,7 (CAR). As a Cooper pair splits into two coupled electrons with opposite spin orientation that are then injected into the two normal-metal leads, instantaneous currents of the same sign are generated across the two SN interfaces, giving rise to a negative non-local resistance as well as a positive current-current correlation between the SN junctions. Previous experimental attempts focused on non-local resistance measurements 8,9,14,15 , but the observation of CAR is complicated by another non-local process called elastic cotunnelling, in which electrons in the normal-metal leads tunnel across the superconductor with the help of Cooper pairs, resulting in a positive non-local resistance and a negative current-current