Unconventional Quantum Hall Effect and Tunable Spin Hall Effect in MoS2 Trilayers

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We analyze the Landau level (LL) structure and spin Hall effect in a MoS2 trilayer. Due to 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 time reversal invariant groups, with LL crossing effects present in the valence bands. We find a field-dependent unconventional Hall plateau sequence ν=... -2M-6, -2M-4, -2M-2, -2M-1,..., -5, -3, -1, 0, 2, 4.... 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.