\textit{Ab initio} studies of influence of periodic-direction electric fields on spin lifetime and spin diffusion length and the validation of an \textit{ab initio} matrix-drift-diffusion model

Abstract

Recently, we developed an \textit{ab initio} approach of spin lifetime (\tau_{s}) and spin diffusion length (l_{s}) in solids [Phys. Rev. Lett. 135, 046705 (2025)], based on a density-matrix master equation with quantum treatment of electron scattering processes. In this work, we extend the method to include the drift term due to an electric field along a periodic direction, implemented using a Wannier-representation-based covariant derivative. We employ this approach to investigate the electric-field effect on \tau_{s} and l_{s} of monolayer WSe_{2}, bulk GaAs, bulk GaN, and graphene-h-BN heterostructure. We find that an electric field reduces \tau_{s} of GaAs, due to the induced D'yakonov-Perel'-type spin relaxation. In GaN and graphene-h-BN, \tau_{s} is significantly affected, partly because the electric field generates an effective magnetic field corresponding to the k-derivative of Rashba spin-orbit (magnetic) field. Our results show that l_{s} can be significantly enhanced or suppressed by a moderate downstream or upstream field respectively. While the standard drift-diffusion model performs well for WSe_{2}, it can introduce large errors of the electric-field-induced changes of l_{s} in GaAs, GaN and graphene-h-BN. Our proposed \textit{ab initio} matrix-drift-diffusion model improves results for GaAs and GaN, but still fails for graphene-h-BN. Thus, to accurately capture the influence of electric fields on l_{s} in realistic materials, it is necessary to go beyond the drift-diffusion model and adopt a microscopic \textit{ab initio} methodology. Moreover, in graphene-h-BN, we find that the field-induced changes of \tau_{s} and l_{s} are not only governed by the drift term in the master equation, but are also significantly affected by the electric-field modification of the equilibrium density matrix away from Fermi-Dirac distribution function.