Double single-channel Kondo coupling in graphene with Fe molecules

We study the interaction between graphene and a single-molecule-magnet, [Fe4(L)2(dpm)6 ]. Focusing on the closest Iron ion in a hollow position with respect to the graphene sheet, we derive a channel selective tunneling Hamiltonian, that couples different d orbitals of the Iron atom to precise independent combinations of sublattice and valley degrees of freedom of the electrons in graphene. When looking at the spin-spin interaction between the molecule and the graphene electrons, close to the Dirac point the channel selectivity results in a channel decoupling of the Kondo interaction, with two almost independent Kondo systems weakly interacting among themselves. The formation of magnetic moments and the development of a full Kondo effect depends on the charge state of the graphene layer