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Carbon based systems are prominent candidates for a solid-state spin-qubitdue to weak spin-orbit and hyperfine interactions in combination with a lownatural abundance of spin carrying isotopes. We consider the effect of thehyperfine interaction on the coherence of an electron-spin localized in agraphene quantum dot. It is known, that the hyperfine interaction in thesesystems is anisotropic promising interesting physics. We calculate the dynamicsof an electron spin surrounded by a bath of nuclear spins in a non-Markovianapproach using a generalized master equation. Considering a general form of thehyperfine interaction, we are able to extend the range of validity of ourresults to other systems beyond graphene. For large external magnetic fields,we find within Born approximation that the electron spin state is conserved upto small corrections, which oscillate with a frequency determined by thehyperfine interaction. The amplitude of these oscillations decays with a powerlaw, where its initial value depends on the specific form of the anisotropy.Analyzing this in more detail, we identify two distinct classes of anisotropy,which can be both found in graphene depending on the orientation of theexternal magnetic field with respect to the carbon layer.

Spin decoherence in graphene quantum dots due to hyperfine interaction