Spin Hall effect driven by the spin magnetic moment current in Dirac materials

The spin Hall effect of a Dirac Hamiltonian system is studied using semiclassical analyses and the Kubo formula. In this system, conductivity dependent on definition current. All components vanish when current defined as flow angular momentum. contrast, off-diagonal are non-zero scale with carrier velocity (and effective $g$-factor) consists magnetic moment. We derive analytical formula conductivity, mobility to compare experiments. experiments, we use Bi model that can be characterized by Hamiltonian. Te Sn doped into vary electron hole concentration, respectively. find ($\sigma_\mathrm{SH}$) takes maximum near point decreases increasing density ($n$). sign $\sigma_\mathrm{SH}$ same regardless majority type. mobility, proportional $\sigma_\mathrm{SH}/n$, increases scaling coefficient $\sim$1.4. These features accounted for quantitatively derived results demonstrate giant moment, an $g$-factor approaches 100, responsible in Bi.