Unconventional quantum hall effect and tunable spin hall effect in Dirac materials: Application to an isolated MoS₂ Trilayer

We analyze the Landau level (LL) structure in a MoS₂ trilayer and find a field-dependent unconventional Hall plateau sequence ν=⋯,-2M-6,-2M-4,-2M-2,-2M-1,⋯,-5,-3,-1,0,2,4,⋯. Because of orbital asymmetry, the low-energy Dirac fermions become heavily massive and the LL energies grow linearly with B, rather than with √B. Spin-orbital couplings break spin and valley degenerate LL's into two groups, with LL crossing effects present in the valence bands. In a p-n junction, spin-resolved fractionally quantized conductance appears in two-terminal measurements with a controllable spin-polarized current that can be probed at the interface. We also show the tunability of zero-field spin Hall conductivity.