  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 bandgap 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 12C, 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.
