Dominance of Extrinsic Scattering Mechanisms in the Orbital Hall Effect: Graphene, Transition Metal Dichalcogenides, and Topological Antiferromagnets

The theory of the orbital Hall effect (OHE), a transverse flow of orbital angular momentum (OAM) in response to an electric field, has concentrated on intrinsic mechanisms. Here, using a quantum kinetic formulation, we determine the full OHE in the presence of short-range disorder using 2D massive Dirac fermions as a prototype. We find that, in doped systems, extrinsic effects associated with the Fermi surface (skew scattering and side jump) provide $\approx 95\%$ of the OHE. This suggests that, at experimentally relevant transport densities, the OHE is primarily extrinsic.

Figure 1

The total, extrinsic, and intrinsic OH conductance ${\sigma }_{\mathrm{OH}}$ vs the Fermi energy $E_F$ for the 2H-phase monolayer ${\mathrm{MoS}}_2$. The parameters are Fermi velocity $v_F=3.6\mathrm{eV}\AA$ and energy gap $2\mathrm{\Delta }=1.766\mathrm{eV}$.

Figure 2

The extrinsic OH conductance ${\sigma }_{\mathrm{OH}}^{\mathrm{ext}}$ vs the Fermi energy $E_F$ for different energy band gaps. For graphene the parameters are $v_F=\frac{3}{2}at$ with $a=1.42\AA$ and $t=2.8\mathrm{eV}$.

Figure 3

The skew scattering and side jump contributions to OH conductance ${\sigma }_{\mathrm{OH}}$ vs the Fermi energy $E_F$: (a) For the 2H-phase monolayer ${\mathrm{MoS}}_2$ with the parameters $v_F=3.6\mathrm{eV}\AA$ and $\mathrm{\Delta }=0.883\mathrm{eV}$; (b) For the tilted 2D massive Dirac model with $v_F=1\mathrm{eV}\AA$ and $\mathrm{\Delta }=0.1\mathrm{eV}$ and $v_t=0.1v_F$. The small tilt correction to the Fermi energy is neglected for small wave vectors.