Substrate effects on spin relaxation in two-dimensional Dirac materials with strong spin-orbit coupling

$$\begin{array}{ll}\dfrac{d{\rho }_{12}\left(t\right)}{dt}\,=\,-\dfrac{i}{\hslash }{\left[{H}_{e},\rho \left(t\right)\right]}_{12}\,+\,\left(\begin{array}{c}\frac{1}{2}{\sum }_{345}\left\{\begin{array}{c}{\left[I-\rho \left(t\right)\right]}_{13}{P}_{32,45}{\rho }_{45}\left(t\right)\\ -{\left[I-\rho \left(t\right)\right]}_{45}{P}_{45,13}^{* }{\rho }_{32}\left(t\right)\end{array}\right\}\\ +H.C.\end{array}\right),\end{array}$$

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