Effective time-reversal symmetry breaking in the spin relaxation in a graphene quantum dot

We study the relaxation of a single electron spin in a circular gate-tunable quantum dot in gapped graphene. Direct coupling of the electron spin to out-of-plane phonons via the intrinsic spin-orbit coupling leads to a relaxation time T-1 which is independent of the B field at low fields. We also find that Rashba spin-orbit induced admixture of opposite spin states in combination with the emission of in-plane phonons provides various further relaxation channels via deformation potential and bond-length change. In the absence of valley mixing, spin relaxation takes place within each valley separately and thus time-reversal symmetry is effectively broken, therefore inhibiting the Van Vleck cancellation at B=0 known from GaAs quantum dots. Both the absence of the Van Vleck cancellation as well as the out-of-plane phonons lead to a behavior of the spin-relaxation rate at low magnetic fields which is markedly different from the known results for GaAs. For low-B fields, we find that the rate is constant in B and then crosses over to alpha B-2 or alpha B-4 at higher fields.