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 Kosterlitz-Thouless 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.
The Kondo effect in the system consisting of a magnetic adatom on the graphene is studied. By using the non-equilibrium Green function method with the slave-boson mean field approximation, the local density of state (LDOS) and the conductance are calculated. For a doped graphene, the Kondo phase is present at all time. Surprisingly, two kinds of Kondo regimes are revealed. But for the undoped graphene, the Kondo phase only exists if the adatom's energy level is beyond a critical value. The conductance is similar to the LDOS, thus, the Kondo peak in the LDOS can be observed with the scanning tu…
We have studied the interplay of an Anderson impurity in Landau quantized graphene, with special emphasis on the influence of the chemical potential. Within the slave-boson mean-field theory, we found reentrant Kondo behaviour by varying the chemical potential or gate voltage. Between Landau levels, the density of states is suppressed, and by changing the graphene's Fermi energy, we cross from metallic to semiconducting regions. Hence, the corresponding Kondo behaviour is also influenced. The f-level spectral function reveals both the presence of Landau levels in the conduction band and the Ko…
We study the Kondo effect of a single magnetic adatom on the surface of graphene. It was shown that the unique linear dispersion relation near the Dirac points in graphene makes it more easy to form the local magnetic moment, which simply means that the Kondo resonance can be observed in a more wider parameter region than in the metallic host. The result indicates that the Kondo resonance indeed can form ranged from the Kondo regime, to the mixed valence, even to the empty orbital regime. While the Kondo resonance displays as a sharp peak in the first regime, it has a peak-dip structure and/or…
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 non-magnetic 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 …
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 ki…
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…
We have studied the effect of dynamical correlations on the electronic structure of single Co adatoms on graphene monolayers with a recently developed novel method for nanoscopic materials that combines density functional calculations with a fully dynamical treatment of the strongly interacting 3d-electrons. The coupling of the Co 3d-shell to the graphene substrate and hence the dynamic correlations are strongly dependent on the orbital symmetry and the system parameters (temperature, distance of the adatom from the graphene sheet, gate voltage). When the Kondo effect takes place, we find that…
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 logarithmi…
We perform a general group-theoretical study of the Kondo problem in monolayer and bilayer graphene around the charge neutrality point. Utilizing the group representation theory, we derive from symmetry considerations a family of the Kondo models for all symmetric placements with either 3- or 6-fold rotational axis of an impurity atom in an arbitrary orbital state. We find six possible classes of the partially anisotropic four-channel Kondo model. As the key result, we argue several possibilities to realize the regime of the dominant channel-symmetric two-channel Kondo effect, protected by the…
We consider the theory of Kondo effect and Fano factor energy dependence for magnetic impurity (Co) on graphene. We have performed a first principles calculation and find that the two dimensional $E_1$ representation made of $d_{xz},d_{yz}$ orbitals is likely to be responsible for the hybridization and ultimately Kondo screening for cobalt on graphene. There are few high symmetry sites where magnetic impurity atom can be adsorbed. For the case of Co atom in the middle of hexagon of carbon lattice we find anomalously large Fano $q$-factor, $q\approx 80$ and strongly suppressed coupling to condu…
We study the localized magnetic states of impurity in biased bilayer and trilayer graphene. It is found that the magnetic boundary for bilayer and trilayer graphene presents the mixing features of Dirac and conventional fermion. For zero gate bias, as the impurity energy approaches the Dirac point, the impurity magnetization region diminishes for bilayer and trilayer graphene. When a gate bias is applied, the dependence of impurity magnetic states on the impurity energy exhibits a different behavior for bilayer and trilayer graphene due to the opening of a gap between the valence and the condu…
Bilayer Kondo systems present interesting models to illustrate the competition between the Kondo effect and intermoment exchange. Such bilayers can exhibit two sharply distinct Fermi liquid phases which are distinguished by whether or not the local moments participate in the Fermi sea. We study these phases and the evolution from one to the other upon changing Kondo coupling. We argue that an ordered state with spontaneous interlayer phase coherence generically intervenes between the two Fermi liquids. Such a condensate phase breaks a U(1) symmetry and is bounded by a finite-temperature Koster…
Localized magnetic moments have been predicted to develop in graphene samples with vacancies or adsorbates. The interplay between such magnetic impurities and graphene's Dirac quasiparticles leads to remarkable many-body phenomena, which have so far proved elusive to experimental efforts. In this article, we study the thermodynamic, spectral and transport signatures of quantum criticality and Kondo physics of a dilute ensemble of atomic impurities in graphene. We consider vacancies and adatoms that either break or preserve graphene's $C_{3v}$ and inversion symmetries. In a neutral graphene sam…
The trigonal zigzag nanodisk with size $N$ has $N$ localized spins. We investigate its thermodynamical properties with and without external leads. Leads are made of zigzag graphene nanoribbons or ordinary metallic wires. There exists a quasi-phase transition between the quasi-ferromagnet and quasi-paramagnet states, as signaled by a sharp peak in the specific heat and in the susceptability. Lead effects are described by the many-spin Kondo Hamiltonian. A new peak emerges in the specific heat. Furthermore, the band width of free electrons in metallic leads becomes narrower. By investigating the…
A bilayer system comprising a Kondo insulator coupled to a simple metal (KI-M) is considered. Employing the framework of dynamical mean field theory, the model system is shown to exhibit a surface of quantum critical points (QCPs), that separates a Kondo screened, Fermi liquid phase from a local moment, Mott insulating phase. The quantum critical nature of these Mott transitions is characterized by the vanishing of (a) the coherence scale on the Fermi liquid side, and (b) the Mott gap on the MI side. In contrast to the usual `large to small' Fermi surface (FS) QCPs in heavy fermion systems, th…
Magnetic impurities in neutral graphene provide a realization of the pseudogap Kondo model, which displays a quantum phase transition between phases with screened and unscreened impurity moment. Here, we present a detailed study of the pseudogap Kondo model with finite chemical potential mu. While carrier doping restores conventional Kondo screening at lowest energies, properties of the quantum critical fixed point turn out to influence the behavior over a large parameter range. Most importantly, the Kondo temperature T_K shows an extreme asymmetry between electron and hole doping. At critical…
We present a simple derivation of a continuum Hamiltonian for bilayer graphene with an arbitrary smooth lattice deformation -- technically in a fashion parametrized by displacement fields with small gradients. We show that this subsumes the continuum model of Bistritzer and Macdonald for twisted bilayer grapheneas well as many generalizations and extensions of it. The derivation is carried out entirely in real space.
We show that the fractional statistics of quasiparticles in dimerized graphene, in recent proposals for charge and statistics fractionalization, can have two realizations depending whether elementary objects can be considered as point-like or extended objects. Therefore, there are two phases of proposed excitations and we give their topological descriptions with their respective statistics. We propose that a natural setting for fractionalization are certain systems with excitonic instabilities and demonstrate this by an example of graphene bilayer.
We have investigated the Coulomb screening properties and collective excitations in a graphene bilayer. The static screening effect is anisotropic and is much stronger in the undoped graphene bilayer than in a monolayer graphene [1]. The dynamic screening shows the properties of a Dirac gas in the low frequency and that of a Fermi gas in the high frequency. The transition from the Dirac to the Fermi gas is also observed in the plasmon spectrum. Finally, we find that an electron gas in a doped graphene bilayer has quite similar properties as those of a Fermi gas in materials containing two ener…
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 $C_{3}$ 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) $\propto 1/ [ | ω\ | \ln ^{2}( Λ/| ω\ | \ ) \ ] $ near the Dirac point $ω\rightarrow …
We show theoretically that graphene, which exhibits a massless Dirac like spectrum for its electrons, can exhibit unconventional Kondo effect that can be tuned by an experimentally controllable applied gate voltage. We demonstrate the presence of a finite critical Kondo coupling strength in neutral graphene. We discuss the possibility of multichannel Kondo effect in this system which might lead to a non-Fermi liquid like ground state and provide a discussion of possible experimental realization of Kondo phenomenon in graphene.
We discuss t-J-U model on a honeycomb monolayer that has the same low-energy description of the kinetic term as graphene bilayer, and in particular study coexistence of antiferromagnetism and superconducting correlations that originate from Cooper pairs without phase coherence. We show that the model is relevant for the description of graphene bilayer and that the presence of the d + i d superconducting correlations with antiferromagnetism can lead to quadratic dependence in small magnetic fields of the gap of the effective monolayer consistent with the transport measurements of Velasco et al.…
In single-layer graphene sheets non-local interband exchange leads to a renormalized Fermi-surface effective mass which vanishes in the low carrier-density limit. We report on a comparative study of Fermi surface effective mass renormalization in single-layer and AB-stacked bilayer graphene. We explain why the mass does not approach zero in the bilayer case, although its value is still strongly suppressed.
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.
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 …
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 k_B ln2 and the expectation value of S^2_z is 1/8.
We study the local moment formation and the Kondo effect at single-atom vacancies in Graphene. We develop a model accounting for the vacancy reconstruction as well as non-planarity effects induced by strain and/or temperature. Thus, we find that the dangling $σ$ orbital localized at the vacancy is allowed to strongly hybridize with the $π$-band since the scattering with the vacancy turns the hybridization into singular function of the energy ($\sim [|ε| \ln^2 ε/D]^{-1}$, $D\sim$ the bandwidth). This leads to several new types of impurity phases, which control the magnitude of the vacancy magne…
Nanoelectronic quantum dot devices exploiting the charge-Kondo paradigm have been established as versatile and accurate analog quantum simulators of fundamental quantum impurity models. In particular, hybrid metal-semiconductor dots connected to two metallic leads realize the two-channel Kondo (2CK) model, in which Kondo screening of the dot charge pseudospin is frustrated. Here, we consider theoretically a two-channel charge-Kondo device made instead from graphene components, realizing a pseudogapped version of the 2CK model. We solve the model using Wilson's Numerical Renormalization Group m…
Bilayer graphene is susceptible to a family of unusual broken symmetry states with spin and valley dependent layer polarization. We report on a microscopic study of the domain walls in these systems, demonstrating that they have interesting microscopic structures related to order-induced topological characters. We use our results to estimate Ginzburg-Landau model parameters and transition temperatures for the ordered states of bilayer graphene.
Using the slave-rotor mean-field theory, we study the formation of Kondo resonance in graphene induced from vacancies. At the Dirac neutrality point, we find acritical hybridization strength beyond which the Kondo resonance takes place, despite vanishing density of states. We also find that the line-shapes of the Kondo peak are entirely different from Lorentzian shown in normal metallic hosts. The dependence of Kondo temperature on the effective hybridization parameter of the spinon field turns out to be linear in contrast to the quadratic dependence in normal metals. Upon doping we find stron…
We investigate Kondo physics in a host with a strongly diverging density of states. This study is motivated by a recent work on vacancies in the graphene honeycomb lattice, whose density of states is enhanced at low energies due to potential scattering. The generalized quantum impurity model describing the vacancy is shown to support a spin-1/2 (doublet) Kondo phase. The special role played by a diverging host density of states is examined in detail, with distinctive signatures associated with the powerlaw Kondo effect shown to appear in thermodynamic quantities and the scattering t matrix, wi…
Based on the non-crossing approximation, we calculate both the linear and nonlinear conductance within the two-lead two-channel single-impurity Anderson model where the conduction electron density of states vanishes in a power-law fashion $ \propto |ω-μ_F|^r$ with $r=1$ near the Fermi energy, appropriate for an hexagonal system. For given gate voltage, we address the universal crossover from a two-channel Kondo phase, argued to occur in doped graphene, to an unscreened local moment phase. We extract universal scaling functions in conductance governing charge transfer through the two-channel ps…
We examine the exchange Hamiltonian for magnetic adatoms in graphene with localized inner shell states. On symmetry grounds, we predict the existence of a class of orbitals that lead to a distinct class of quantum critical points in graphene, where the Kondo temperature scales as $T_{K}\propto|J-J_{c}|^{1/3}$ near the critical coupling $J_{c}$, and the local spin is effectively screened by a \emph{super-ohmic} bath. For this class, the RKKY interaction decays spatially with a fast power law $\sim1/R^{7}$. Away from half filling, we show that the exchange coupling in graphene can be controlled …
We study the impurity states in bilayer graphene in the unitary limit using Green's function method. Unlike in single layer graphene, the presence of impurities at two non-equivalent sites in bilayer graphene produce different impurity states which is understood as the change in the band structure due to interlayer hopping of electrons. The impurity states can also be tuned by changing the band structure of bilayer grahene through external electric field bias.
A detailed analysis of the Kondo effect of a magnetic impurity in a zigzag graphene nanoribbon is addressed. An adatom is coupled to the graphene nanoribbon via a hybridization amplitude $Γ_{imp}$ in a hollow or top site configuration. In addition, the adatom is also weakly coupled to a metallic STM tip by a hybridization function $Γ_{tip}$ that provides a Kondo screening of its magnetic moment. The entire system is described by an Anderson-like Hamiltonian whose low-temperature physics is accessed by employing the numerical renormalization group approach, which allows us to obtain the thermod…
High-harmonic generation (HHG) in solids is an emerging method to probe ultrafast electron dynamics in solids at attosecond timescale. In this work, we study HHG from monolayer and bilayer graphene. Bilayer graphenes with AA and AB stacking are considered in this work. It is found that the monolayer and bilayer graphenes exhibit significantly different harmonic spectra. The difference in the spectra is attributed to the interlayer coupling between the two layers. Also, the intraband and interband contributions to the total harmonic spectrum play a significant role. Moreover, interesting polari…
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 app…
Bilayer graphene has been predicted to give unprecedented tunability of the electron-electron interaction with the help of external parameters, allowing one to stabilize different fractional quantum Hall states. Recent experimental works make theoretical analysis of such systems extremely relevant. In this paper we describe a methodology for investigating the possibility of realizing specific fractional quantum Hall states in bilayer graphene taking into account polarization effects and virtual interband transitions. We apply this methodology to explore the possibility of realizing the Moore-R…
We study single hole dynamics in the bilayer Heisenberg and Kondo Necklace models. Those models exhibit a magnetic order-disorder quantum phase transition as a function of the interlayer coupling J_perp. At strong coupling in the disordered phase, both models have a single-hole dispersion relation with band maximum at p = (π,π) and an effective mass at this p-point which scales as the hopping matrix element t. In the Kondo Necklace model, we show that the effective mass at p = (π,π) remains finite for all considered values of J_perp such that the strong coupling features of the dispersion rela…
The nature of superconductivity in heavy-fermion materials is a subject under intense debate, and controlling this many-body state is central for its eventual understanding. Here, we examine how proximity effects may change this phenomenon, by investigating the effects of an additional metallic layer on the top of a Kondo-lattice, and allowing for pairing in the former. We analyze a bilayer Kondo Lattice Model with an on-site Hubbard interaction, $-U$, on the additional layer, using a mean-field approach. For $U=0$, we notice a drastic change in the density-of-states due to multiple-orbital si…
Experiments on graphene bilayers, where the top layer is rotated with respect to the one below, have displayed insulating behavior when the moiré bands are partially filled. We calculate the charge distributions in these phases, and estimate the excitation gaps.
We study theoretically the Kondo effect for a magnetic adatom on graphene using the Anderson model.Upon obtaining the Green's function of the impurity to higher order contributions in the hybridization, we calculated analytically the selfenergy in the presence of strong correlations.It is found that the Kondo resonance takes place in a narrow energy range of the impurity level around the Fermi energy which can be tuned by a gate voltage.We show that this range is linear in the Fermi energy $|μ|$ and is significantly narrower than in the case for a normal metal.The origin of this behavior is tr…
The X-ray edge singularity of bilayer graphene is studied by generalizing the path integral approach based on local action which was employed for monolayer graphene. In sharp contrast to the case of monolayer graphene, the bilayer graphene is found to exhibit the edge singularity even at half-filling and its characteristics are determined by interlayer coupling. At finite bias the singular behaviors sensitively depend on the relative magnitude of fermi energy and applied bias, which is due to the peculiar shape of energy band at finite bias.
The cooperative behavior of quantum impurities on 2D materials, such as graphene and bilayer graphene, is characterized by a non-trivial competition between screening (Kondo effect), and Ruderman-Kittel-Kasuya-Yosida (RKKY) magnetism. In addition, due to the small density of states at the Fermi level, impurities may not couple to the conduction electrons at all, behaving as free moments. Employing a recently developed {\em{exact}} numerical method to study multi-impurity lattice systems, we obtain non-perturbative results that dramatically depart from expectations based on the conventional RKK…
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 ef…
The interaction between a magnetic impurity, such as cerium (Ce) atom, and surrounding electrons has been one of the core problems in understanding many-body interaction in solid and its relation to magnetism. Kondo effect, the formation of a new resonant ground state with quenched magnetic moment, provides a general framework to describe many-body interaction in the presence of magnetic impurity. In this Letter, a combined study of angle-resolved photoemission (ARPES) and dynamic mean-field theory (DMFT) on Ce-intercalated graphene shows that Ce-induced localized states near Fermi energy, $E_…
The Kondo effect typically arises from the spin-flip scattering between the localized magnetic moment of the impurity and the delocalized electrons in the metallic host, which leads to a variety of intriguing phenomena. Here, by using scanning tunnelling microscopy/spectroscopy (STM/STS), we present the Kondo effect and subatomic features of single U adatom on graphene/6H-SiC(0001). A dip spectral feature can be observed around the Fermi energy, which is termed as the "fingerprint" of the Kondo resonance in STS; in addition, two subatomic features with different symmetries: a three-lobe struct…
