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Spin to pseudo-spin conversion by which spin population imbalance converts tonon-equilibrium pseudo-spin density in Dirac systems has been investigatedparticularly for graphene and insulator phase of silicene. Calculations havebeen performed within the Kubo approach and by taking into account the vertexcorrection. Results indicate that spin converts to pseudo-spin in eithergraphene or silicene that identified to come from the spin-orbit interactions.The response function of spin to pseudo-spin conversion is weakened severalorders of magnitude by vertex correction of impurities in graphene, however,this conversion is strengthened in insulator silicene. In addition, in the caseof silicene, results are indicative of an obvious change in the mentionedresponse function as a result of the change in band-topology which can beobserved by manipulation of external electric field, vertically applied to thesystem surface. At the critical electric field in which the topological phasetransition for silicene nano-ribbon has been observed, response functionchanges abruptly. Interconversion between the quantum numbers could provide afield for information and data processing technologies.

Spin to pseudo-spin conversion in graphene-like systems: A Kubo formalism including vertex corrections