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We study the dynamics of an electron spin in a graphene quantum dot, which isinteracting with a bath of less than ten nuclear spins via the anisotropichyperfine interaction. Due to substantial progress in the fabrication ofgraphene quantum dots, the consideration of such a small number of nuclearspins is experimentally relevant. This choice allows us to use exactdiagonalization to calculate the longtime average of the electron spin as wellas its decoherence time. We investigate the dependence of spin observables onthe initial states of nuclear spins and on the position of nuclear spins in thequantum dot. Moreover, we analyze the effects of the anisotropy of thehyperfine interaction for different orientations of the spin quantization axiswith respect to the graphene plane. Interestingly, we then predict remarkablelong decoherence times of more than 10ms in the limit of few nuclear spins.

Ultra long spin decoherence times in graphene quantum dots with a small number of nuclear spins