Theory of Defect-Induced Kondo Effect in Graphene: Numerical Renormalization Group Study

Kanao, Taro; Matsuura, Haruaki; Ogata, Masao

doi:10.1143/jpsj.81.063709

Cited by 37 publications

(72 citation statements)

References 24 publications

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“…Also, it is surprising that the transport data could be fitted to theoretical results for metallic Kondo screening even near neutrality where standard single-parameter scaling is not expected due to strong energy dependence of the host DOS. Despite interesting proposals and ideas [62,63], we feel that a convincing theoretical explanation for the results of Ref. [59] is missing to date.…”

Section: Defectsmentioning

confidence: 82%

The physics of Kondo impurities in graphene

Fritz¹,

Vojta²

2013

Rep. Prog. Phys.

145

197

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Abstract. This article summarizes our understanding of the Kondo effect in graphene, primarily from a theoretical perspective. We shall describe different ways to create magnetic moments in graphene, either by adatom deposition or via defects. For dilute moments, the theoretical description is in terms of effective Anderson or Kondo impurity models coupled to graphene's Dirac electrons. We shall discuss in detail the physics of these models, including their quantum phase transitions and the effect of carrier doping, and confront this with existing experimental data. Finally, we point out connections to other quantum impurity problems, e.g., in unconventional superconductors, topological insulators, and quantum spin liquids.arXiv:1208.3113v2 [cond-mat.str-el]

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Section: Defectsmentioning

confidence: 82%

The physics of Kondo impurities in graphene

Fritz¹,

Vojta²

2013

Rep. Prog. Phys.

145

197

View full text Add to dashboard Cite

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“…(15) and used to describe H Q1D AIM in Eq. (19). The "on-site potential" and "nearest-neighbor hopping" matrices,Ê l andT l , respectively, in Eq.…”

Section: B Symmetrization Of Bl Basesmentioning

confidence: 99%

“…One of the possible explanations of the emergent magnetic moment in graphene with a structural defect is due to the partially filled dangling bonds of sp 2 orbital on carbon atoms surrounding the vacancy [19][20][21][22][23][24][25]. It has been also pointed out that the scattering of defects drastically changes the electronic structures of π band and produces the logarithmic divergence at E F in the local density of states at the vicinity of defects [21,26,27].…”

Section: Introductionmentioning

confidence: 99%

Block Lanczos density-matrix renormalization group method for general Anderson impurity models: Application to magnetic impurity problems in graphene

Shirakawa

Yunoki

2014

Phys. Rev. B

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We introduce a block Lanczos (BL) recursive technique to construct quasi-one-dimensional models, suitable for density-matrix renormalization group (DMRG) calculations, from single-as well as multiple-impurity Anderson models in any spatial dimensions. This new scheme, named BL-DMRG method, allows us to calculate not only local but also spatially dependent static and dynamical quantities of the ground state for general Anderson impurity models without losing elaborate geometrical information of the lattice. We show that the BL-DMRG method can be easily extended to treat a multiorbital Anderson impurity model where not only inter-and intraorbital Coulomb interactions but also Hund's coupling and pair hopping interactions are included. We also show that the symmetry adapted BL bases can be utilized, when it is appropriate, to reduce the computational cost. As a demonstration, we apply the BL-DMRG method to three different models for graphene with a structural defect and with a single hydrogen or fluorine absorbed, where a single Anderson impurity is coupled to conduction electrons in the honeycomb lattice. These models include (i) a single adatom on the honeycomb lattice, (ii) a substitutional impurity in the honeycomb lattice, and (iii) an effective model for a single carbon vacancy in graphene. Our analysis of the local dynamical magnetic susceptibility and the local density of states at the impurity site reveals that, for the particle-hole symmetric case at half-filling of electron density, the ground state of model (i) behaves as an isolated magnetic impurity with no Kondo screening, while the ground state of the other two models forms a spin-singlet state where the impurity moment is screened by the conduction electrons. We also calculate the real-space dependence of the spin-spin correlation functions between the impurity site and the conduction sites for these three models. Our results clearly show that, reflecting the presence or absence of unscreened magnetic moment at the impurity site, the spin-spin correlation functions decay as ∝ r −3 , differently from the noninteracting limit (∝ r −2 ), for model (i) and as ∝ r −4 , exactly the same as the noninteracting limit, for models (ii) and (iii) in the asymptotic r, where r is the distance between the impurity site and the conduction site. Finally, based on our results, we shed light on recent experiments on graphene where the formation of local magnetic moments as well as the Kondo-like behavior have been observed.

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“…The technologically and conceptually important issue of creating localized magnetic moments in monolayer graphene, and the appearance of the Kondo effect, have been the focus of many recent theoretical [9][10][11][12][13][14][15][16][17][18][19][20] and experimental [21][22][23][24] studies, with controversial results (see [25] for an overview). A more complex DOS appears in bilayer graphene (BLG), a material that can be gapped by gating, and thus has attracted much attention for possible device applications [26].…”

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confidence: 99%

Quantum phase transitions into Kondo states in bilayer graphene

et al. 2014

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We study a magnetic impurity intercalated in bilayer graphene. A representative configuration generates a hybridization function with strong dependence on the conduction-electron energy, including a full gap with one hard and one soft edge. Shifts of the chemical potential via gating or doping drive the system between non-Kondo (free-moment) and Kondo-screened phases, with strong variation of the Kondo scale. Quantum phase transitions near the soft edge are of KosterlitzThouless type, while others are first order. Near the hard edge, a bound-state singlet appears inside the gap; although of single-particle character, its signatures in scanning tunneling spectroscopy are very similar to those arising from a many-body Kondo resonance.PACS numbers: 72.15. Qm, 73.22.Pr, 75.20.Hr, 64.70.Tg One of the remarkable manifestations of cooperative phenomena in condensed matter is the many-body screening of a magnetic impurity in a nonmagnetic metal. This Kondo effect, well understood in ordinary metals [1], acquires added complexity in cases where the host density of states (DOS) varies strongly with energy E near the chemical potential µ. The pseudogap Kondo problem [2-6] with a DOS ρ(E) ∝ |E − µ| r (realized, for example, for r = 1 in high-temperature superconductors [7]) exhibits a rich phase diagram that depends on the band exponent r, the impurity-host exchange coupling J, and the presence or absence of particle-hole (p-h) symmetry.Similar DOS features can also appear in lowdimensional systems such as graphene [8]. The technologically and conceptually important issue of creating localized magnetic moments in monolayer graphene, and the appearance of the Kondo effect, have been the focus of many recent theoretical [9][10][11][12][13][14][15][16][17][18][19][20] and experimental [21][22][23][24] studies, with controversial results (see [25] for an overview). A more complex DOS appears in bilayer graphene (BLG), a material that can be gapped by gating, and thus has attracted much attention for possible device applications [26]. The variety of microscopic environments for magnetic impurities combined with easy tunability, make BLG highly promising for the study of quantum phase transitions (QPTs) into various Kondo states [27,28].This paper explores such QPTs for a representative configuration of an intercalated spin σ = 1/2 magnetic impurity in BLG. This setup is described by an Anderson impurity model with an energy-dependent hybridization featuring a gap that has one hard and one soft edge. Under variation of the chemical potential µ, the system passes from a free-moment (FM) phase to a Kondo phase featuring a strong µ dependence of the Kondo temperature scale. The QPTs found near the soft hybridization edge are of Kosterlitz-Thouless type, while all other QPTs are first order. We present thermodynamic and spectral properties near these QPTs, and discuss some of their consequences for spectroscopy measurements. For µ near the hard hybridization edge, the FM phase exhibits a singlet bound state inside the gap. This bo...

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Theory of Defect-Induced Kondo Effect in Graphene: Numerical Renormalization Group Study

Cited by 37 publications

References 24 publications

The physics of Kondo impurities in graphene

The physics of Kondo impurities in graphene

Block Lanczos density-matrix renormalization group method for general Anderson impurity models: Application to magnetic impurity problems in graphene

Quantum phase transitions into Kondo states in bilayer graphene

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