We analyze non-local effects in electron transport across three-terminal normal-superconductingnormal (NSN) structures. Subgap electrons entering S-electrode from one N-metal may form Cooper pairs with their counterparts penetrating from another N-metal. This phenomenon of crossed Andreev reflection -combined with normal scattering at SN interfaces -yields two different contributions to non-local conductance which we evaluate non-perturbatively at arbitrary interface transmissions. Both these contributions reach their maximum values at fully transmitting interfaces and demonstrate interesting features which can be tested in future experiments.At sufficiently low temperatures Andreev reflection (AR) [1] dominates charge transfer through an interface between a normal metal and a superconductor (NS): An electron propagating from the normal metal with energy below the superconducting gap ∆ enters the superconductor at a length of order of the superconducting coherence length ξ, forms a Cooper pair together with another electron, while a hole goes back into the normal metal. As a result, the net charge 2e is transferred through the NS interface which acquires non-zero subgap conductance [2].

We report a theoretical study on the deviations of the Meissner penetration depth λ(T ) from its London value in d-wave superconductors at low temperatures. The difference arises from low-energy surface Andreev bound states. The temperature dependent penetration depth is shown to go through a minimum at the temperature Tm0 ∼ ξ0/λ0Tc if the broadening of the bound states is small. The minimum will straighten out when the broadening reaches Tm0. The impurity scattering sets up the low-temperature anomalies of the penetration depth and destroys them when the mean free path is not sufficiently large. A phase transition to a state with a spontaneous surface supercurrent is investigated and its critical temperature determined in the absence of a subdominant channel activated at low temperatures near the surface. Nonlinear corrections from Andreev low-energy bound states to the penetration length are obtained and shown, on account of their broadening, to be small in the Meissner state of strong type II superconductors.

We formulate a microscopic theory of nonlocal electron transport in three-terminal diffusive normal-superconducting-normal (NSN) structures with arbitrary interface transmissions. At low energies epsilon, we predict strong enhancement of nonlocal spectral conductance g_{12} proportional, variant1/epsilon due to quantum interference of electrons in disordered N terminals. In contrast, nonlocal resistance R_{12} remains smooth at small epsilon and, furthermore, is found to depend neither on parameters of normal-superconducting interfaces nor on those of N terminals. At higher temperatures, R_{12} exhibits a peak caused by the trade-off between charge imbalance and Andreev reflection. Our results are in a good agreement with recent experimental observations and can be used for quantitative analysis of future experiments.

We develop a detailed microscopic theory describing dc Josephson effect and Andreev bound states in superconducting junctions with a half metal. In such systems, the supercurrent is caused by triplet pairing states emerging due to spin-flip scattering at the interfaces between superconducting electrodes and the half metal. For sufficiently clean metals, we provide a detailed nonperturbative description of the Josephson current at arbitrary transmissions and spin-flip scattering parameters for both interfaces. Our analysis demonstrates that the behavior of both the Josephson current and Andreev bound states crucially depends on the strength of spin-flip scattering, showing a rich variety of features which can be tested in future experiments.

With the aid of the quasiclassical Eilenberger formalism we develop a theory of non-local electron transport across three-terminal ballistic normal-superconducting-normal (NSN) devices with spin-active NS interfaces. The phenomenon of crossed Andreev reflection (CAR) is known to play the key role in such transport. We demonstrate that CAR is highly sensitive to electron spins and yields a rich variety of properties of non-local conductance which we describe non-perturbatively at arbitrary voltages, temperature, spin-dependent interface transmissions and their polarizations. Our results can be applied to multi-terminal hybrid structures with normal, ferromagnetic and half-metallic electrodes and can be directly tested in future experiments.Comment: 11 pages, 7 figures; figures 6 and 7 are corrected; version published in Phys. Rev.