▎ 摘　　要

The study of spin-related phenomena in materials requires knowledge of the precise form of effective spin-orbit coupling for conducting carriers in solid-state systems. We demonstrate theoretically that curvature induced by corrugations or periodic ripples in single-layer graphenes generates two types of effective spin-orbit couplings. In addition to the spin-orbit coupling reported previously that couples with sublattice pseudospin and corresponds to the Rashba-type spin-orbit coupling in a corrugated single-layer graphene, there is an additional spin-orbit coupling that does not couple with the pseudospin, which can not be obtained from the extension of the curvature-induced spin-orbit coupling of carbon nanotubes. Via numerical calculation we show that both types of the curvature-induced spin-orbit coupling make the same order of contribution to spin relaxation in chemically clean single-layer graphene with nanoscale corrugation. The spin-relaxation dependence on the corrugation roughness is also studied.