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The study of spin-related phenomena in materials requires knowledge on theprecise form of effective spin-orbit coupling of conducting carriers in thesolid-states systems. We demonstrate theoretically that curvature induced bycorrugations or periodic ripples in single-layer graphenes generates two typesof effective spin-orbit coupling. In addition to the spin-orbit couplingreported previously that couples with sublattice pseudospin and corresponds tothe Rashba-type spin-orbit coupling in a corrugated single-layer graphene,there is an additional spin-orbit coupling that does not couple with thepseudospin, which can not be obtained from the extension of thecurvature-induced spin-orbit coupling of carbon nanotubes. Via numericalcalculation we show that both types of the curvature-induced spin-orbitcoupling make the same order of contribution to spin relaxation in chemicallyclean single-layer graphene with nanoscale corrugation. The spin relaxationdependence on the corrugation roughness is also studied.

Curvature-induced spin-orbit coupling and spin relaxation in a chemically clean single-layer graphene