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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.
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 t
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 d
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 whic
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 a
Cooper pair splitters are promising candidates for generating spin-entangled electrons. However, the splitting of Cooper pairs is a random and noisy process, which hinders further synchronized operations on the entangled electrons. To circumvent this