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Thermoelectric effect is exploited to optimize the Cooper pair splitting efficiency in a Y-shaped junction, which consists of two normal leads coupled to an $s$-wave superconductor via double noninteracting quantum dots. Here, utilizing temperature difference rather than bias voltage between the two normal leads, and tuning the two dot levels such that the transmittance of elastic cotunneling process is particle-hole symmetric, we find currents flowing through the normal leads are totally contributed from the splitting of Cooper pairs emitted from the superconductor. Such a unitary splitting efficiency is significantly better than the efficiencies obtained in experiments so far.
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In this paper, we demonstrate that the hybrid normal-superconducting-normal (NSN) structure has potential for a multifunctional thermal device which could serve for heat flux control and cooling of microstructures. By adopting the scattering matrix approach, we theoretically investigate thermal and electrical effects emerging in such structures due to the Cooper pair splitting (CPS) and elastic cotunneling phenomena. We show that a finite superconductor can, in principle, mediate heat flow between normal leads, and we further clarify special cases when this seems contradictory to the second law of thermodynamics. Among other things, we demonstrate that the CPS phenomenon can appear even in the simple case of a ballistic NSN structure.
We consider ballistic SQUIDs with spin filtering inside half-metallic ferromagnetic arms. A singlet Cooper pair cannot pass through an arm in this case, so the Josephson current is entirely due to the Cooper pair splitting, with two electrons going to different interferometer arms. In order to elucidate the mechanisms of Josephson transport due to split Cooper pairs, we assume the arms to be single-channel wires in the short-junction limit. Different geometries of the system (determined by the length of the arms and the phases acquired by quasiparticles during splitting between the arms) lead to qualitatively different behavior of the SQUID characteristics (the Andreev levels, the current-phase relation, and the critical Josephson current) as a function of two control parameters, the external magnetic flux and misorientation of the two spin filters. The current-phase relation can change its amplitude and shape, in particular, turning to a pi-junction form or acquiring additional zero crossings. The critical current can become a nonmonotonic function of the misorientation of the spin filters and the magnetic flux (on half of period). Periodicity with respect to the magnetic flux is doubled, in comparison to conventional SQUIDs.
We study Josephson junctions with weak links consisting of two parallel disordered arms with magnetic properties -- ferromagnetic, half-metallic or normal with magnetic impurities. In the case of long links, the Josephson effect is dominated by mesoscopic fluctuations. In this regime, the system realises a $varphi_0$ junction with sample-dependent $varphi_0$ and critical current. Cooper pair splitting between the two arms plays a major role and leads to $2Phi_0$ periodicity of the current as a function of flux between the arms. We calculate the current and its flux and polarization dependence for the three types of magnetic links.
At the interface between a ferromagnetic insulator and a superconductor there is a coupling between the spins of the two materials. We show that when a supercurrent carried by triplet Cooper pairs flows through the superconductor, the coupling induces a magnon spin current in the adjacent ferromagnetic insulator. The effect is dominated by Cooper pairs polarized in the same direction as the ferromagnetic insulator, so that charge and spin supercurrents produce similar results. Our findings demonstrate a way of converting Cooper pair supercurrents to magnon spin currents.
Bilayer graphene hosts valley-chiral one dimensional modes at domain walls between regions of different interlayer potential or stacking order. When such a channel is brought into proximity to a superconductor, the two electrons of a Cooper pair which tunnel into it move in opposite directions because they belong to different valleys related by the time-reversal symmetry. This is a kinetic variant of Cooper pair splitting, which requires neither Coulomb repulsion nor energy filtering but is enforced by the robustness of the valley isospin in the absence of atomic-scale defects. We derive an effective model for the guided modes in proximity to an s-wave superconductor, calculate the conductance carried by split and spin-entangled electron pairs, and interpret it as a result of local Andreev reflection processes, whereas crossed Andreev reflection is absent.
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