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Valley- and spin-switch effects in molybdenum disulfide superconducting spin valve

We propose a hole-doped molybdenum disulfide (MoS$_2$) superconducting spin valve (F/S/F) hybrid structure in which the Andreev reflection process is suppressed for all incoming waves with a determined range of the chemical potential in ferromagnetic (F) region and the cross-conductance in the right F region depends crucially on the configuration of magnetizations in the two F regions. Using the scattering formalism, we find that the transport is mediated purely by elastic electron cotunneling (CT) process in a parallel configuration and changes to the pure crossed Andreev reflection (CAR) process in the low-energy regime, without fixing of a unique parameter, by reversing the direction of magnetization in the right F region. This suggests both valley- and spin-switch effects between the perfect elastic CT and perfect CAR processes and makes the nonlocal charge current to be fully valley- and spin-polarized inside the right F region where the type of the polarizations can be changed by reversing the magnetization direction in the right F region. We further demonstrate that the presence of the strong spin-orbit interaction $λ$ and an additional topological term ($β$) in the Hamiltonian of MoS$_2$ result in an enhancement of the charge conductance of the CT and CAR processes and make them to be present for long lengths of the superconducting region. Besides, we find that the thermal conductance of the structure with a small length of the highly doped superconducting region exhibits linear dependence on the temperature at low temperatures whereas it enhances exponentially at higher temperatures. In particular, we demonstrate that the thermal conductance versus the strength of the exchange field ($h$) in F region displays a maximum value at $h<λ$, which moves towards larger exchange fields by increasing the temperature.