Enhanced Spin-Flip Scattering by Surface Roughness in WS$_2$ and MoS$_2$ Nanoribbons

The band structures of single-layer MoS$_2$ and WS$_2$ present a coupling between spin and valley degrees of freedom that suppresses spin-flip scattering and spin dephasing. Here we show that out-of-plane deformations, such as corrugations or ripples, enhance spin-flip scattering. Spin transport in armchair MoS$_2$ and WS$_2$ nanoribbons in the presence of surface roughness is systematically investigated, employing the non-equilibrium Green's function method along with the tight-binding approximation. Both transmission and magnetoresistance have been calculated as a function of surface roughness. Our results indicate that the spin-flip rate, usually neglected in flat pristine samples, increases significantly with the surface roughness amplitude. These results are important for the design and fabrication of transition metal dicalcogenides based spintronic devices.