We study valley polarization, spin, and valley Hall conductivity in doped monolayer MoS2 considering dopant introduced magnetic exchange field using low energy effective Hamiltonian. We found that dopant introduced magnetic exchange field breaks the time inversion symmetry and decouples the energetically degenerated valleys into nondegenerate. Moreover, the calculated result reveals that, at low temperature, in insulating regime, anomalous Hall conductivity in a single valley and the total valley Hall conductivity are quantized, whereas the total spin Hall conductivity vanishes identically. We also found that the strength of the spin-orbit coupling together with the exchange field determines the valley polarization, which in turn controls valley and spin Hall conductivity in doped monolayer MoS2 system. The spin Hall and valley Hall conductivity is dissipationless in the absence of any external magnetic field. Therefore, our results are crucial to generate low power electronics devices.
Asymmetric Andreev resonant state with a magnetic exchange field in spin-triplet superconducting monolayer MoS 2
