Electron spin relaxation in graphene nanoribbon quantum dots

Graphene is promising as a host material for electron spin qubits because of its predicted potential for long coherence times. In armchair graphene nanoribbons (aGNRs) a small band gap is opened, allowing for electrically gated quantum dots, and furthermore the valley degeneracy is lifted. The spin lifetime $T_1$ is limited by spin relaxation, where the Zeeman energy is absorbed by lattice vibrations, mediated by spin-orbit and electron-phonon coupling. We have calculated $T_1$ by treating all couplings analytically and find that $T_1$ can be in the range of seconds for several reasons: (i) low phonon density of states away from Van Hove singularities; (ii) destructive interference between two relaxation mechanisms; (iii) Van Vleck cancellation at low magnetic fields; (iv) vanishing coupling to out-of-plane modes in lowest order due to the electronic structure of aGNRs. Owing to the vanishing nuclear spin of ${}^{12}$C, $T_1$ may be a good measure for overall coherence. These results and recent advances in the controlled production of graphene nanoribbons make this system interesting for spintronics applications.