Cooper pair splitting in diffusive magnetic 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 $2\Phi_0$ 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. 
P. A. Ioselevich, P. M. Ostrovsky, Ya. V. Fominov, M. V. Feigelman
cond-mat.mes-hall cond-mat.supr-con