Kondo Effect In Graphene Research Articles

Tunable Kondo Resonance at a Pristine Two-Dimensional Dirac Semimetal on a Kondo Insulator.

The proximity of two different materials leads to an intricate coupling of quasiparticles so that an unprecedented electronic state is often realized at the interface. Here, we demonstrate a resonance-type many-body ground state in graphene, a nonmagnetic two-dimensional Dirac semimetal, when grown on SmB6, a Kondo insulator, via thermal decomposition of fullerene molecules. This ground state is typically observed in three-dimensional magnetic materials with correlated electrons. Above the characteristic Kondo temperature of the substrate, the electron band structure of pristine graphene remains almost intact. As temperature decreases, however, the Dirac Fermions of graphene become hybridized with the Sm 4f states. Remarkable enhancement of the hybridization and Kondo resonance is observed with further cooling and increasing charge-carrier density of graphene, evidencing the Kondo screening of the Sm 4f local magnetic moment by the conduction electrons of graphene at the interface. These findings manifest the realization of the Kondo effect in graphene by the proximity of SmB6 that is tuned by the temperature and charge-carrier density of graphene.

Ferromagnetism-induced Kondo effect in graphene with a magnetic impurity

We investigate the many-body effects of a magnetic adatom in ferromagnetic graphene by using the numerical renormalization group method. The nontrivial band dispersion of ferromagnetic graphene gives rise to interesting Kondo physics different from that in conventional ferromagnetic materials. For a half-filled impurity in undoped graphene, the presence of ferromagnetism can bring forth Kondo correlations, yielding two kink structures in the local spectral function near the Fermi energy. When the spin splitting of local occupations is compensated by an external magnetic field, the two Kondo kinks merge into a full Kondo resonance characterizing the fully screened ground state. Strikingly, we find the resulting Kondo temperature monotonically increases with the spin polarization of Dirac electrons, which violates the common sense that ferromagnetic bands are usually detrimental to Kondo correlations. Doped ferromagnetic graphene can behave as half metals, where its density of states at the Fermi energy linearly vanishes for one spin direction but keeps finite for the opposite direction. In this regime, we demonstrate an abnormal Kondo resonance that occurs in the first spin direction, while completely absent in the other one.

Modeling the Kondo effect of a magnetic atom adsorbed on graphene

The Kondo effect due to a magnetic atom adsorbed on graphene is investigated using two theoretical approaches, including the non-equilibrium Green’s function method within the slave-boson mean-field approximation and a newly developed tight-binding (TB) model with an effectively infinite Hubbard U term. Both methods reveal the presence of a Kondo peak in the local density of state (LDOS) of graphene near the Fermi level. A sharp Kondo peak is only observed in the odd-neighboring C sites of the C atom directly below the magnetic atom placed in top position. The peak intensity is found to decay quickly with respect to the distance between the C site and the magnetic atom. A theoretical model of scanning tunneling microscopy (STM) of graphene is presented as a means to identify the manifestation of the Kondo effect via direct topographic STM measurements. STM simulations show that in the proximity of the magnetic atom, only the C atoms of one sublattice are visible at low bias potential and thus a triangular lattice can be seen, in agreement with recent experiments. Further away from the magnetic atom, the Kondo effect dies down and eventually both sublattices are visible, leading to the recovery of the hexagonal lattice. This work not only provides a new TB method to study the Kondo effect in graphene, but also presents both scanning tunneling spectroscopy and microscopy fingerprints of the Kondo effect to facilitate its experimental verification.

Defect-induced Kondo effect in graphene: role of localized state of π electrons

We discuss a role of the localized π orbital, which exists around the defect, on the defect-induced Kondo effect in graphene by a numerical renormalization group study. We find that the localized π orbital assists this Kondo effect, and the Kondo temperature is sensitive to the broadening of the localized π orbital. Secondly, we focus on the negative magnetoresistance of this Kondo effect. In the experimental result, it has been shown that the negative magnetoresistance is ten times larger than the usual Kondo effect. In order to clarify the mechanism of the ’’magnetic sensitive” Kondo effect, as a first step, we study an orbital magnetic field dependence of the localized n orbital by a tight-binding model with a Peierls phase. We find that as the magnetic field increases, the spectral width of the localized π orbital increases and the local DOS at the Fermi level decreases. Since the Kondo temperature is strongly dependent of the broadening of the localized π orbital, it is expected that this Kondo effect is sensitive to the orbital magnetic field as observed in the experiment.

Disorder-mediated Kondo effect in graphene

We study the emergence of strongly correlated states and Kondo physics in disordered graphene. Diluted short range disorder gives rise to localized midgap states at the vicinity of the system charge neutrality point. We show that long-range disorder, ubiquitous in graphene, allows for the coupling of these localized states to an effective (disorder averaged) metallic band. The system is described by an Anderson-like model. We use the numerical renormalization group (NRG) method to study the distributions of Kondo temperatures $P(T_K)$. The results show that disorder can lead to long logarithmic tails in $P(T_K)$, consistent with a quantum Griffiths phase.

Kondo effect in graphene with Rashba spin-orbit coupling

We study the Kondo screening of a magnetic impurity adsorbed in graphene in the presence of Rashba spin-orbit interaction. The system is described by an effective single-channel Anderson impurity model, which we analyze using the numerical renormalization group. The nontrivial energy dependence of the host density of states gives rise to interesting behaviors under variation of the chemical potential or the spin-orbit coupling. Varying the Rashba coupling produces strong changes in the Kondo temperature characterizing the many-body screening of the impurity spin, and at half filling allows approach to a quantum phase transition separating the strong-coupling Kondo phase from a free-moment phase. Tuning the chemical potential close to sharp features of the hybridization function results in striking features in the temperature dependences of thermodynamic quantities and in the frequency dependence of the impurity spectral function.

Gate-tunable Kondo resistivity and dephasing rate in graphene studied by numerical renormalization group calculations

Motivated by the recent observation of the Kondo effect in graphene in transport experiments, we investigate the resistivity and dephasing rate in the Kondo regime due to magnetic impurities in graphene with different chemical potentials ($\ensuremath{\mu}$). The Kondo effect due to either carbon vacancies or magnetic adatoms in graphene is described by the single-orbital pseudogap asymmetric Anderson impurity model which is solved by the accurate numerical renormalization group method. We find that although the Anderson impurity model considered here is a mixed-valence system, it can be driven into either the Kondo [$\ensuremath{\mu}>{\ensuremath{\mu}}_{c}$ (critical value) $>0$], mixed-valency ($\ensuremath{\mu}\ensuremath{\approx}{\ensuremath{\mu}}_{c}$), or empty-orbital ($\ensuremath{\mu}<{\ensuremath{\mu}}_{c}$) regime by a gate voltage, giving rise to characteristic features in resistivity and dephasing rate in each regime. Specifically, in the case of $\ensuremath{\mu}<{\ensuremath{\mu}}_{c}$, the shapes of the resistivity (dephasing rate) curves for different $\ensuremath{\mu}$ are nearly identical. However, as temperature decreases, they start to increase to their maxima at a lower $T/{T}_{K}$, but more rapidly [as ${({T}_{K}/T)}^{3/2}$] than in normal metals [here, $T$ (${T}_{K}$) denotes the (Kondo) temperature]. As $T$ further decreases, after reaching the maximum, the dephasing rate drops more quickly than in normal metals, behaving as ${(T/{T}_{K})}^{3}$ instead of ${(T/{T}_{K})}^{2}$. Furthermore, the resistivity has a distinct peak above the saturation value near ${T}_{K}$. In the case of $\ensuremath{\mu}>{\ensuremath{\mu}}_{c}$, in contrast, the resistivity curve has an additional broad shoulder above 10${T}_{K}$ and the dephasing rate exhibits an interesting shoulder-peak shape. In the narrow boundary region ($\ensuremath{\mu}\ensuremath{\approx}{\ensuremath{\mu}}_{c}$), both the resistivity and dephasing rate curves are similar to the corresponding ones in normal metals. This explains the conventional Kondo-like resistivity from recent experiments on graphene with defects, although the distinct features in the resistivity in the other cases ($\ensuremath{\mu}<{\ensuremath{\mu}}_{c}$ or $\ensuremath{\mu}>{\ensuremath{\mu}}_{c}$) were not seen in the experiments. The interesting features in the resistivity and dephasing rate are analyzed in terms of the calculated $T$-dependent spectral function, correlation self-energy, and renormalized impurity level.

Detection of the Kondo effect in the resistivity of graphene: Artifacts and strategies

We discuss the difficulties to discover Kondo effect in the resistivity of graphene. Similarly to the Kondo effect, electron-electron interaction effects and weak localization appear as logarithmic corrections to the resistance. In order to disentangle these contributions, a refined analysis of the magnetoconductance and the magnetoresistance is introduced. We present numerical simulations which display the discrimination of both effects. Further, we present experimental data of magnetotransport. When magnetic molecules are added to graphene, a logarithmic correction to the conductance occurs, which apparently suggests Kondo physics. Our thorough evaluation scheme, however, reveals that this interpretation is not conclusive: the data can equally be explained by electron-electron interaction corrections in an inhomogeneous sample. Our evaluation scheme paves the way for a more refined search for the Kondo effect in graphene.

Theory of Defect-Induced Kondo Effect in Graphene: Effect of Zeeman Field

The effect of the Zeeman field on the defect-induced Kondo effect in graphene is investigated. The effective model of the Kondo effect is derived, and is analyzed on the basis of the numerical renormalization group method. It is found that, under the Zeeman field, at the border of the spin polarized state and the Kondo-Yosida singlet state, there is an unusual fixed point where the entropy of the defect is kB ln 2 and the expectation value of S2z is 1/8.

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

An effective model that describes the Kondo effect due to a point defect in graphene is developed, taking account of the electronic state and the lattice structure of the defect. It is shown that this model can be transformed into a single-channel pseudogap Anderson model with a finite chemical potential. On the basis of the numerical renormalization group method, it is clarified that the experimentally observed gate-voltage dependence of the Kondo temperature is understood in this framework.

Tunable Kondo effect in graphene with defects

Graphene is a model system for the study of electrons confined to a strictly two-dimensional layer1 and a large number of electronic phenomena have been demonstrated in graphene, from the fractional2, 3 quantum Hall effect to superconductivity4. However, the coupling of conduction electrons to local magnetic moments5, 6, a central problem of condensed matter physics, has not been realized in graphene, and, given carbon's lack of d or f electrons, magnetism in graphene would seem unlikely. Nonetheless, magnetism in graphitic carbon in the absence of transition-metal elements has been reported7-10, with explanations ranging from lattice defects11 to edge structures12, 13 to negative curvature regions of the graphene sheet14. Recent experiments suggest that correlated defects in highly-ordered pyrolytic graphite (HOPG) induced by proton irradiation9 or native to grain boundaries7, can give rise to ferromagnetism. Here we show that point defects (vacancies) in graphene15 are local moments which interact strongly with the conduction electrons through the Kondo effect6, 16-18 providing strong evidence that defects in graphene are indeed magnetic. The Kondo temperature TK is tunable with carrier density from 30-90 K; the high TK is a direct consequence of strong coupling of defects to conduction electrons in a Dirac material18. The results indicate that defect engineering in graphene could be used to generate and control carrier-mediated magnetism, and realize all-carbon spintronic devices. Furthermore, graphene should be an ideal system in which to probe Kondo physics in a widely tunable electron system.

Orbitally controlled Kondo effect of Co adatoms on graphene

Based on ab-initio calculations we identify possible scenarios for the Kondo effect due to Co ad-atoms on graphene. General symmetry arguments show that for magnetic atoms in high-symmetry positions, the Kondo effect in graphene is controlled not only by the spin but also by the orbital degree of freedom. For a Co atom absorbed on top of a carbon atom, the Kondo effect is quenched by spin-orbit coupling below an energy scale of $\sim 15$\,K. For Co with spin $S=1/2$ located in the center of a hexagon, an SU(4) Kondo model describes the entanglement of orbital moment and spin at higher energies, while below \sim 60$\,meV spin-orbit coupling leads to a more conventional SU(2) Kondo effect. The interplay of the orbital Co physics and the peculiar band-structure of graphene is directly accessible in Fourier transform tunneling spectroscopy or in the gate-voltage dependence of the Kondo temperature displaying a very strong, characteristic particle-hole asymmetry.

Orthogonality catastrophe and Kondo effect in graphene

Anderson's orthogonality catastrophe [Phys. Rev. Lett. 18, 1049 (1967)] in graphene, at energies close to the Dirac point, is analyzed. It is shown that, in clean systems, the orthogonality catastrophe is suppressed due to the vanishing density of states at the Dirac point. In the presence of preexisting localized states at the Dirac energy, the orthogonality catastrophe shows features similar to those found in normal metals with a finite density of states at the Fermi level. The implications for the Kondo effect induced by magnetic impurities, and for the Fermi edge singularities in tunneling processes, are also discussed.