2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/25878We propose a nonequilibrium Green's function approach to study the spin-Hall effect in a two-dimensional electron system with both the Rashba and Dresselhaus spin-orbit couplings. By taking into account the long-range electron-impurity scattering, the derived kinetic equations are solved numerically. It is found the vanishing of the total zero-temperature dissipationless spin-Hall effect, contributing from the intrinsic and disorder-mediated processes. This result has been examined in the wide ranges of spin-orbit coupling constants and electron density.5 pages, 1 figureMaterials ScienceMesoscale and Nanoscale Physicstext