Pure valley- and spin-entangled states in a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">MoS</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>-based bipolar transistor

In this study, we show that the local Andreev reflection not only can be tuned largely by the type of the normal metal electrode, it also is related to the electrostatic potential in the superconductor region in a ${\mathrm{MoS}}_{2}$-based $n(p)$-type metal/superconductor junction. In a ${\mathrm{MoS}}_{2}$-based $n$-type metal/$n(p)$-type superconductor/$p$-type metal $(\mathrm{n}\text{S}\mathrm{p})$ transistor, nonlocal pure valley- and spin-entangled current can be tuned by the length and local gate voltage of a superconductor region. In particular, switching the quasiparticle type in both structures results in a series of intriguing features. Such an effect is not attainable in a graphene-based junction where the electron-hole symmetry enables the symmetry results to be observed. Besides, we have shown that the crossed Andreev reflection exhibits a maximum around $\ensuremath{\xi}/2$ instead of the exponential decay behavior in conventional superconductors and a maximum around $\ensuremath{\xi}$ in the graphene material. The proposed straightforward experimental design and pure valley- and spin-entangled state can pave the way for a wider use in the entanglement based on material group-VI dichalcogenides.