Extrinsic, disorder-driven orbital Hall conductivity dominates at high doping in bilayer MoS2, and a gate voltage that breaks inversion symmetry strongly amplifies it.
It can be seen from this formula that the intrinsic term has a finite value for the in-gap Fermi energy
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Comparing the Extrinsic Orbital Hall Effect in Centrosymmetric and Noncentrosymmetric Systems: Insights from Bilayer Transition Metal Dichalcogenides
Extrinsic, disorder-driven orbital Hall conductivity dominates at high doping in bilayer MoS2, and a gate voltage that breaks inversion symmetry strongly amplifies it.