We theoretically investigate the supercurrent through a Josephson junction with at least one superconducting electrode directly coupled to a valley-polarized graphene sheet. The anomalous Josephson effect is shown and remarkably manipulated by interface valley-polarized mixing together with combination of the static staggered potentials and off-resonant circularly polarized light field inducing the valley polarization. The unconventional Josephson effect results from the breaking of underlying chiral (polarized-valley rotational) and time-reversal symmetries, which in turn shows the equivalence of the valley and spin freedoms. The valley-polarized interfacetunable phase offset will be of great interest in the designing and fabrication of such novel devices based on valleytronics as superconducting flux-and phase-based quantum bits, phase batteries and rectifiers.

For Entangled electron pairs superconducting spintronics, there exist two drawbacks in existing proposals of generating entangled electron pairs. One is that the two kinds of different spin entangled electron pairs mix with each other. And the other is a low efficiency of entanglement production. Herein, we report the spin entanglement state of the ferromagnetic insulator (FI)/s-wave superconductor/FI structure on a narrow quantum spin Hall insulator strip. It is shown that not only the high production of entangled electron pairs in wider energy range, but also the perfect spin filtering of entangled electron pairs in the context of no highly spin-polarized electrons, can be obtained. Moreover, the currents for the left and right leads in the antiferromagnetic alignment both can be zero, indicating 100% tunnelling magnetoresistance with highly magnetic storage efficiency. Therefore, the spin filtering for entangled electron pairs and magnetic storage with high efficiencies coexist in one setup. The results may be experimentally demonstrated by measuring the tunnelling conductance and the noise power.

An extended four-component Bogoliubov-de Gennes equation is applied to study the Josephson effect in ballistic limit between either two iron-based superconductors (SCs) or an iron-based SC and a conventional s-wave SC, separated by a normal metal. A 0-π transition as a function of interband coupling strength α is always exhibited, arising from the tuning of mixing between the two trajectories with opposite phases. The novel property can be experimentally used to discriminate the s  -wave pairing symmetry in the iron-based SCs from the s ++ -wave one in MgB 2 . The effect of interface transparency on the 0-π transition is also presented. The 0-π transition as a function of α is wholly distinct from that as a function of barrier strength or temperature in recent theories (Linder et al 2009 Phys. Rev. B 80 020503(R)). The possible experimental probe of the phase-shift effect in iron-based SC Josephson junctions is commented on as well.