We investigate the crossed Andreev reflection (CAR) in a zigzag graphene nanoribbon/superconductor/nanoribbon junction. It is shown that when the zigzag chain number of the ribbon is even and only the zero-energy mode is involved in transport, either the elastic cotunneling or the local Andreev reflection could be entirely suppressed by using a gate voltage whereas a sizeable CAR is achieved. When one of the ribbon leads is magnetized, not only the CAR is exclusive but also the spin state of the CAR transmission is nonlocally controllable. The physical origin is the peculiar valley selection rule in the even zigzag graphene nanoribbon. The ideal Cooper-pair splitting in the proposed device holds for all applied bias in the superconducting energy gap.
We theoretically investigate the quantum Hall effect in a graphene superlattice (GS) system, in which the two valleys of graphene are coupled together. In the presence of a perpendicular magnetic field, an ordinary quantum Hall effect is found with the sequence σxy = νe 2 /h(ν = 0, ±1, ±2, • • • ). At the zeroth Hall platform, a valley-chiral Hall state stemming from the single K or K valley is found and it is localized only on one sample boundary contributing to the longitudinal conductance but not to the Hall conductivity. Our findings may shed light on the graphene-based valleytronics applications.
The spin of Majorana fermions (MF) is nearly frozen by the applied magnetic field in a composite 1D topological superconductor due to the weak spin-orbit coupling (SOC). In this work, we address theoretically the strong SOC limit and weak-magnetic-field effect, under which the spin degree of freedom of MFs is reactivated and dependent on the wire direction. The quantized zero-energy conductance peak in a bent N/S wire junction can be severely suppressed. The MF phase is significantly modified due to the spin noncollinearity and the fusion of MFs is independent of the wire direction, which is opposite to the strong-magnetic-field case. It is also found that the spatial distribution of an MF could be heavily affected by the wire direction. The findings are helpful to identify and braid MFs in the 1D wire network.
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