Kondo effect due to a hydrogen impurity in graphene: A multichannel Kondo problem with diverging hybridization

Abstract

We consider the Kondo effect arising from a hydrogen impurity in graphene. As a first approximation, the strong covalent bond to a carbon atom removes that carbon atom without breaking the C3 rotation symmetry, and we only retain the Hubbard interaction on the three nearest neighbors of the removed carbon atom which then behave as magnetic impurities. These three impurity spins are coupled to three conduction channels with definite helicity, two of which support a diverging local density of states (LDOS) ∝ 1/ |ω| ln 2 (Λ/ |ω|) near the Dirac point ω → 0 even though the bulk density of states vanishes linearly. We study the resulting 3-impurity multichannel Kondo model using the numerical renormalization group method. For weak potential scattering, the ground state of the Kondo model is a particle-hole symmetric spin-1/2 doublet, with ferromagnetic coupling between the three impurity spins; for moderate potential scattering, the ground state becomes a particle-hole asymmetric spin singlet, with antiferromagnetic coupling between the three impurity spins. This behavior is inherited by the Anderson model containing the hydrogen impurity and all four carbon atoms in its vicinity. arXiv:1907.05331v2 [cond-mat.str-el]

Renormalization of spin excitations and Kondo effect in open-shell nanographenes

“…Note that the NG hosts the localized electrons, while the conduction electrons are in the substrate. This is different from the case of the Kondo effect of magnetic impurities and point defects in graphene [43][44][45][46][47][48][49].…”

Renormalization of spin excitations and Kondo effect in open shell nanographenes

“…Note that the NG hosts the localized electrons, while the conduction electrons are in the substrate. This is different from the case of Kondo effect of magnetic impurities and point defects in graphene [41][42][43][44].…”

Poor man’s scaling: XYZ Coqblin–Schrieffer model revisited

“…As Nr approaches unity, the third-order terms in the equation become important, and the fixed points equations (33) and (34) eventually merge with strong-coupling fixed points, similar to the situation in the nchannel pseudogap Kondo model [37]. On the other hand, the fixed points equations (30) and (31) stay in the weak-coupling regime as long as r/N 1; in the spirit of [24] it is therefore reasonable to argue that the maximum r, for which the weak-coupling analysis is applicable, increases with the number of channels N .…”

“…On the other hand, the maximum r below which our perturbative approach qualitatively applies cannot be extracted from the perturbation theory itself. Numerical renormalization group studies [25,28] find that the nontrivial fixed point is absent for r 1/2; this includes the linear density of states r = 1 as is the case in bulk graphene, although the Kondo problem in graphene is further complicated by the presence of multiple conduction channels and the honeycomb lattice [26,27,[29][30][31]35].…”

“…We also take into account a possible power-law energy dependence of the density of states of itinerant electrons at the Fermi energy (i.e. a pseudogap density of states) [20,[24][25][26][27][28][29][30][31], which can arise in semimetals, nodal superconductors as well as one-dimensional interacting systems.…”