Unconventional Quantum Hall Effect and Tunable Spin Hall Effect in Dirac Materials: Application to an IsolatedMoS2Trilayer

Abstract

We analyze the Landau level (LL) structure in a ${\mathrm{MoS}}_{2}$ trilayer and find a field-dependent unconventional Hall plateau sequence $\ensuremath{\nu}=\dots{},\ensuremath{-}2M\ensuremath{-}6,\ensuremath{-}2M\ensuremath{-}4,\ensuremath{-}2M\ensuremath{-}2,\ensuremath{-}2M\ensuremath{-}1,\dots{},\ensuremath{-}5,\ensuremath{-}3,\ensuremath{-}1,0,2,4,\dots{}$. Because of orbital asymmetry, the low-energy Dirac fermions become heavily massive and the LL energies grow linearly with $B$, rather than with $\sqrt{B}$. Spin-orbital couplings break spin and valley degenerate LL's into two groups, with LL crossing effects present in the valence bands. In a $p\mathrm{\text{\ensuremath{-}}}n$ 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.