Electron spin diffusion in monolayer MoS$_2$

Electron spin diffusion is investigated in monolayer MoS$_2$ in the absence of external electric and magnetic fields. The electron-impurity scattering, which is shown to play a negligible role in spin relaxation in time domain in this material, has a marked effect on the in-plane spin diffusion due to the anisotropic spin precession frequency in the spatial domain. With the electron-impurity and inter-valley electron-phonon scatterings separately included in the scattering term, we study the intra- and inter-valley diffusion processes of the in-plane spins by analytically solving the kinetic spin Bloch equations. The intra-valley process is found to be dominant in the in-plane spin diffusion, in contrast to the case of spin relaxation in time domain, where the inter-valley process can be comparable to or even more important than the intra-valley one. For the intra-valley process, we find that the in-plane spin diffusion is suppressed with the increase of impurity density but effectively enhanced by increasing electron density in both the degenerate and nondegenerate limits. We also take into account the electron-electron Coulomb scattering in the intra-valley process. Interestingly, we find that in the nondegenerate limit, the intra-valley spin diffusion length presents an opposite trend in the electron density dependence compared to the one with only electron-impurity scattering.