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Recently, the existence of local magnetic moment in a hydrogen adatom ongraphene has been confirmed experimentally [Gonz\'{a}lez-Herrero et al.,Science, 2016, 352, 437]. Inspired by this breakthrough, we theoreticallyinvestigate the top-site adatom on trilayer graphene (TLG) by solving theAnderson impurity model via self-consistent mean field method. The influence ofthe stacking order, the adsorption site and external electric field arecarefully considered. We find that, due to its unique electronic structure, thesituation of the TLG is drastically different from that of the monolayergraphene. Firstly, the adatom on rhombohedral stacked TLG (r-TLG) can have aFano-shaped impurity spectral density, instead of the normal Lorentzian-likeone, when the impurity level is around the Fermi level. Secondly, the impuritylevel of the adatom on r-TLG can be tuned into an in-gap state by an externalelectric field, which strongly depends on the direction of the applied electricfield and can significantly affect the local magnetic moment formation.Finally, we systematically calculate the impurity magnetic phase diagrams,considering various stacking orders, adsorption sites, doping and electricfield. We show that, because of the in-gap state, the impurity magnetic phaseof r-TLG will obviously depend on the direction of the applied electric fieldas well. All our theoretical results can be readily tested in experiment, andmay give a comprehensive understanding about the local magnetic moment ofadatom on TLG.

Fano-shaped impurity spectral density, electric-field-induced in-gap state and local magnetic moment of an adatom on trilayer graphene