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We investigate the spin relaxation and decoherence in a single-electrongraphene quantum dot with Rashba and intrinsic spin-orbit interactions. Wederive an effective spin-phonon Hamiltonian via the Schrieffer-Wolfftransformation in order to calculate the spin relaxation time T_1 anddecoherence time T_2 within the framework of the Bloch-Redfield theory. In thismodel, the emergence of a non-monotonic dependence of T_1 on the externalmagnetic field is attributed to the Rashba spin-orbit coupling-inducedanticrossing of opposite spin states. A rapid decrease of T_1 occurs when thespin and orbital relaxation rates become comparable in the vicinity of thespin-mixing energy-level anticrossing. By contrast, the intrinsic spin-orbitinteraction leads to a monotonic magnetic field dependence of the spinrelaxation rate which is caused solely by the direct spin-phonon couplingmechanism. Within our model, we demonstrate that the decoherence time T_2 ~ 2T_1 is dominated by relaxation processes for the electron-phonon couplingmechanisms in graphene up to leading order in the spin-orbit interaction.Moreover, we show that the energy anticrossing also leads to a vanishing purespin dephasing rate for these states for a super-Ohmic bath.

Non-monotonic spin relaxation and decoherence in graphene quantum dots with spin-orbit interactions