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Valley Zeeman effect and spin-valley polarized conductance in monolayer MoS$_2$ in a perpendicular magnetic field

We study the effect of a perpendicular magnetic field on the electronic structure and charge transport of a monolayer MoS$_2$ nanoribbon at zero temperature. We particularly explore the induced valley Zeeman effect through the coupling between the magnetic field, $B$, and the orbital magnetic moment. We show that the effective two-band Hamiltonian provides a mismatch between the valley Zeeman coupling in the conduction and valence bands due to the effective mass asymmetry and it is proportional to $B^2$ similar to the diamagnetic shift of exciton binding energies. However, the dominant term which evolves with $B$ linearly, originates from the multi-orbital and multi-band structures of the system. Besides, we investigate the transport properties of the system by calculating the spin-valley resolved conductance and show that, in a low-hole doped case, the transport channels at the edge are chiral for one of the spin components. This leads to a localization of the non-chiral spin component in the presence of disorder and thus provides a spin-valley polarized transport induced by disorder.