We consider the problem of electron energy states related to strongly localized potential of a single impurity in graphene. Our model simulates the effect of impurity atom substituting the atom of carbon, on the energy spectrum of electrons near the Dirac point. We take into account the internal spin-orbit interaction, which can modify the structure of electron bands at very small neighborhood of the Dirac point, leading to the energy gap. This makes possible the occurrence of additional impurity states in the vicinity of the gap.
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.
We investigate a magnetic impurity in Bernal stacked bilayer graphene by a non-perturbative numerical exact approach. In the two cases we study, impurity is placed on the top of two different sublattices (A and B) in bilayer graphene. We find that similar to the monolayer case, magnet moment of the impurity could still be tuned in a wide range through changing the chemical potential. However, the property of the impurity depends strongly on its location due to the broken symmetry between sublattices A and B caused by the Bernal stacking. This difference becomes more apparent with the increase …
We study the property of a magnetic impurity on a single-layer graphene within an Anderson impurity model. Due to the vanishing local density of states at the Fermi level in graphene, the impurity spin cannot be effectively screened out. Treating the problem within the Gutzwiller approximation, we found a region in the parameter space of $U$-$E^f$ where the impurity is in the local moment state, which is characterized by a zero effective hybridization between the bath electron and the magnetic impurity. Here $U$ is the onsite Coulomb repulsion of the impurity electrons and $E^f$ the impurity e…
With a conserving formalism within the self-consistent Born approximation, we study the Hall conductivity of Dirac fermions in graphene under charged impurity scatterings. The calculated inverse Hall coefficient is compared with the experimental data. It is shown that the present calculations for the Hall coefficient and the electric conductivity are in good agreement with the experimental measurements.
It is pointed out that point defects on graphene are strongly correlated and can not be treated as independent scatters. In particular, for large on-site defect potential, it is shown that defects induce an impurity band with density of state characterized by the Wigner semi-circle law. We find that the impurity band enhances conductivity to the order of $4 e^2 /h $ and explains the absence of strong localization. Furthermore,the impurity band supports ferromagnetism with the induced magnetic moment approaching 1$μ_B$ per defect in the limit of infinite quasi-particle lifetime.
We address the problem of a Coulomb impurity in graphene in the presence of a perpendicular uniform magnetic field. We show that the problem can be solved below the supercritical impurity magnitude within the WKB approximation. Without impurity the semiclassical energies correctly reproduce the Landau level spectrum. For a given Landau level the WKB energy depends on the absolute value of angular momentum in a way which is consistent with the exact diagonalization result. Below the supercritical impurity magnitude, the WKB solution can be expanded as a convergent series in powers of the effect…
On the basis of self-consistent Born approximation, we solve the Bethe-Salpeter matrix equations for Cooperon propagator of the Dirac fermions in graphene under the charged impurity scatterings and a weak external magnetic field. In the absence of the magnetic field, the quantum interference effect in the electric conductivity from the contribution of Cooperon propagator will be studied and possible weak localization in the system is discussed in terms of the sample length and temperature. The magnetoconductivity stemming from the quantum interference effect is calculated, and the obtained res…
Defect-induced magnetic moments are at the center of the research effort on spintronic applications of graphene. Here we study the problem of a nonmagnetic impurity in graphene with a new theoretical method, inhomogeneous cluster dynamical mean field theory (I-CDMFT), which takes into account interaction-induced short-range correlations while allowing long-range inhomogeneities. The system is described by a Hubbard model on the honeycomb lattice. The impurity is modeled by a local potential. For a large enough potential, interactions induce local antiferromagnetic correlations around the impur…
We consider a graphene sheet in the presence of a strong perpendicular magnetic field with a single short-range delta-impurity situated at one of the carbon sites. We study the neutral inter-Landau level collective excitations, magnetoplasmons, which become localized on the impurity. Some of these excitations involve a pseudospin flip (intervalley transitions), since the impurity can scatter electrons between the two valleys. We propose a classification of states of the excitations in graphene and introduce the appropriate quantum numbers. The energies and optical strengths of collective excit…
We used a quantum Monte Carlo method to study the magnetic impurity adatoms on graphene. We found that by tuning the chemical potential we could switch the values of the impurity's local magnet moment between relatively large and small values. Our computations of the impurity's spectral density found its behavior to differ significantly from that of an impurity in a normal metal and our computations of the charge-charge and spin-spin correlations between the impurity and the conduction band electrons found them to be strongly suppressed. In general our results are consistent with those from po…
We use quantum Monte Carlo method to study a magnetic impurity located next to a vacancy in bilayer graphene with Bernal stacking. Due to the broken symmetry between two sublattices in bilayer system, there exist two different types of vacancy induced localized state. We find that the magnetic property of the adatom located on the adjacent site of the vacancy depends on whether the vacancy belongs to A or B sublattice. In general, local moment is more strongly suppressed if the vacancy belongs to the sublattice A when $μ\sim 0$. We switch the values of the chemical potential and study the basi…
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 multi-orbital Anderso…
Based on the tight-binding formalism, we investigate the Anderson and the Kondo model for an adaom magnetic impurity above graphene. Different impurity positions are analyzed. Employing a partial wave representation we study the nature of the coupling between the impurity and the conducting electrons. The components from the two Dirac points are mixed while interacting with the impurity. Two configurations are considered explicitly: the adatom is above one atom (ADA), the other case is the adatom above the center the honeycomb (ADC). For ADA the impurity is coupled with one flavor for both A a…
With quantum Monte Carlo methods, we investigate the consequences of placing a magnetic adatom adjacent to a vacancy in a graphene sheet. We find that instead of the adatom properties depending on the energy of the adatom orbital, as in a single impurity problem, they develop a dependence on the energy of the split localized state associated with the single vacancy problem. Shifting the chemical potential through this experimentally more accessible energy scale reveals novel behavior in the spectral density, magnetic susceptibility, and the correlations of the adatom spin and charge with those…
The Anderson model of an $s$-wave single-orbital correlated impurity placed on a noninteracting honeycomb lattice, a simplified model for studying an impurity on graphene, is used to investigate pseudogap Kondo problem. In this model, there are two quantum phases: the phase of free impurity local moment and the Kondo phase where this local moment is fully screened. The transition between these two phases is under investigation. The work focuses mostly on the case where the impurity is placed on top of a lattice site. In this case, the full phase diagram is constructed using three parameters: t…
We study theoretically the physical properties of a magnetic impurity in graphene. Within the Anderson model for a very strong Coulomb interaction on the impurity, we start from the Slave-Boson method and introduce a topological picture consisting of a degree of a map and a winding number (WN) to analyze the phase shift and the occupation on the impurity. The occupation is linked to WN. For a generic normal metal we find a fractional WN. In contrast, the winding is accelerated by the relativistic dispersion of graphene at half-filling leading to an integer occupation. We show that the renormal…
We consider the problem of screening of an electrically charged impurity in a clean graphene sheet. When electron-electron interactions are neglected, the screening charge has a sign opposite to that of the impurity, and is localized near the impurity. Interactions between electrons smear out the induced charge density to give a large-distance tail that follows approximately, but not exactly, an r^{-2} behavior and with a sign which is the same as that of the impurity.
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…
In the low-energy two-band as well as four-band continuum models, we study the supercritical instability in gapped bilayer graphene in the field of a charged impurity. It is found that the screening effects are crucially important in bilayer graphene. If they are neglected, then the critical value for the impurity charge as the lowest-energy bound state dives into the lower continuum tends to zero as the gap $Δ$ vanishes. If the screened Coulomb interaction is considered, then the critical charge tends to a finite value for $Δ\to 0$. The different scalings of the kinetic energy of quasiparticl…
The problem of a magnetic impurity, atomic or molecular, absorbed on top of a carbon atom in otherwise clean graphene is studied using the numerical renormalization group. The spectral, thermodynamic, and scattering properties of the impurity are described in detail. In the presence of a small magnetic field, the low energy electronic features of graphene make possible to inject spin polarized currents through the impurity using a scanning tunneling microscope (STM). Furthermore, the impurity scattering becomes strongly spin dependent and for a finite impurity concentration it leads to spin po…
The plasmon modes of pristine and impurity doped graphene are calculated, using a real-space theory which determines the non-local dielectric response within the random phase approximation. A full diagonalization of the polarization operator is performed, allowing the extraction of all its poles. It is demonstrated how impurities induce the formation of localized modes which are absent in pristine graphene. The dependence of the spatial modulations over few lattice sites and frequencies of the localized plasmons on the electronic filling and impurity strength is discussed. Furthermore, it is s…
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…
In this work, we study the magnetic-impurity resonance states in superconducting phase of twisted bilayer graphene for different pairing symmetries. Using the two-orbital model proposed by Yuan and Fu in [Phys. Rev. B 98, 045103 (2018)], we find that when the impurity is located at one site of the emergent honeycomb lattice, the spacial distributions of the resonance states will break both the threefold and twofold rotation symmetries of $D_3$ group for pairing symmetries which belong to the irreducible representations of this point group. When the magnetic impurity is located at the center of…
In this paper, by considering the Hubbard model on a honeycomb lattice, we developed a theory for the intrinsic magnetic impurities (MIs) with the quasi-localized spin moments induced by the vacancies in graphene. Because the intrinsic MIs are characterized by the zero modes that are rthotropic to the itinerant electrons, their properties are much different from those of Anderson MIs with the well-localized spin moments.
The electron states in the field of a charged impurity in graphene in a magnetic field are studied numerically. It is shown that a charged impurity removes the degeneracy of Landau levels converting them into bandlike structures. As the charge of impurity grows, the repulsion of sublevels of different Landau levels with the same value of orbital momentum takes place leading to the redistribution of the wave function profiles of these sublevels near the impurity. By studying the polarization effects, it is shown in agreement with the recent experiments that the effective charge of impurity can …
The local properties of bilayer graphene (BLG) due to the spatial inhomogeneity of its sublattices are of interest. We apply Anderson impurity model to consider the local moment formation on a magnetic impurity which could be adsorbed on different sublattices of BLG. We find different features for the impurity magnetization when it is adsorbed A and B sublattices. The impurity adsorbed on A sublattice can magnetize even when the impurity level is above the Fermi level and the on-site coulomb energy is very small. But when the impurity is adsorbed on B sublattice the magnetization is possible f…
We address the problem of an unscreened Coulomb charge in graphene, and calculate the local density of states and displaced charge as a function of energy and distance from the impurity. This is done non-perturbatively in two different ways: (1) solving the problem exactly by studying numerically the tight-binding model on the lattice; (2) using the continuum description in terms of the 2D Dirac equation. We show that the Dirac equation, when properly regularized, provides a qualitative and quantitative low energy description of the problem. The lattice solution shows extra features that canno…
Based on the tight-binding formalism, we investigate the Anderson and the Kondo model for an adaom magnetic impurity above graphene. Different impurity positions are analyzed. Employing a partial wave representation we study the nature of the coupling between the impurity and the conducting electrons. The components from the two Dirac points are mixed while interacting with the impurity. Two configurations are considered explicitly: the adatom is above one atom (ADA), the other case is the adatom above the center the honeycomb (ADC). For ADA the impurity is coupled with one flavor for both A a…
Triple point fermions are elusive electronic excitations that generalize Dirac and Weyl modes beyond the conventional high energy paradigm. Yet, finding real materials naturally hosting these excitations at the Fermi energy has remained challenging. Here we show that twisted bilayer graphene is a versatile platform to realize robust triple point fermions in two dimensions. In particular, we establish that the introduction of localized impurities lifts one of the two degenerate Dirac cones, yielding triple point fermions at charge neutrality. Furthermore, we show that the valley polarization is…
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 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…
In this work the effects of impurity in various insulating phases of the twisted bilayer graphene (TBG) are studied. The well-accepted continuum model\cite{b} is employed and the local density of states (DOS) is calculated. It is found that insulating phases breaking different symmetries proposed in previous theories\cite{pa,op1,Lee_2019} are distinguishable via the number and properties of in-gap bound state peaks induced by impurities in local DOS. Insulating phases breaking the same previously proposed symmetries can be further classified by the remaining anti-unitary symmetries and disting…
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…
The effect of substitution atoms on the energy spectrum and the electrical conductivity of graphene was investigated in a Lifshitz one-electron tight-binding model. It is established that the ordering of impurity atoms results in a gap in the energy spectrum of electrons whose width depends on the order parameter and on the magnitude of the scattering potential. It is shown that if the order parameter is close to its maximum value, there are peaks associated with localized impurity states on the energy curve of the electron states density at the edges of the energy gap. At the electron concent…
We study the electric and thermal transport of the Dirac carriers in monolayer graphene using the Boltzmann-equation approach. Motivated by recent thermopower measurements [F. Ghahari, H.-Y.~Xie, T. Taniguchi, K. Watanabe, M.~S.~Foster, and P.~Kim, Phys.\ Rev.\ Lett.\ {\bf 116}, 136802 (2016)], we consider the effects of quenched disorder, Coulomb interactions, and electron--optical-phonon scattering. Via an unbiased numerical solution to the Boltzmann equation we calculate the electrical conductivity, thermopower, and electronic component of the thermal conductivity, and discuss the validity …
We calculate the indirect charge carrier mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities for two selected graphene nanoflakes containing four hexagonal rings in their structure, differing by their geometry. We describe the electronic structure of either charge-neutral or doped nanoflakes using the tight-binding approximation with the Hubbard term, which is treated within the molecular-field approximation. We find pronounced differences in the RKKY coupling energies, dependent on the placement of the pair of magnetic moments in the nanostructure and on the …
We present exact analytical and numerical results for the electronic spectra and the Friedel oscillations around a substitutional impurity atom in a graphene lattice. A chemical dopant in graphene introduces changes in the on-site potential as well as in the hopping amplitude. We employ a T-matrix formalism and find that disorder in the hopping introduces additional interference terms around the impurity that can be understood in terms of bound, semi-bound, and unbound processes for the Dirac electrons. These interference effects can be detected by scanning tunneling microscopy.
The {}^{17}O NMR spectra of Bi_2Sr_2CaCu_2O$_{8+δ}$ (Bi-2212) single crystals were measured in the temperature range from 4 K to 200 K and magnetic fields from 3 to 29 T, reported here principally at 8 T. The NMR linewidth of the oxygen in the CuO_{2} plane was found to be magnetically broadened with the temperature dependence of a Curie law where the Curie coefficient decreases with increased doping. This inhomogeneous magnetism is an impurity effect intrinsic to oxygen doping and persists unmodified into the superconducting state.
We explore theoretically the density of states (LDOS) probed by an STM tip of 2D systems hosting an adatom and a subsurface impurity,both capacitively coupled to AFM tips and traversed by antiparallel magnetic fields. Two kinds of setups are analyzed, a monolayer of graphene and a two-dimensional electron gas (2DEG). The AFM tips set the impurity levels at the Fermi energy, where two contrasting behaviors emerge: the Fano factor for the graphene diverges, while in the 2DEG it approaches zero. As result, the spin-degeneracy of the LDOS is lifted exclusively in the graphene system, in particular…
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 address local inelastic scattering from vibrational impurity adsorbed onto graphene and the evolution of the local density of electron states near the impurity from weak to strong coupling regime. For weak coupling the local electronic structure is distorted by inelastic scattering developing peaks/dips and steps. These features should be detectable in the inelastic electron tunneling spectroscopy, $d^2I/dV^2$, using local probing techniques. Inelastic Friedel oscillations distort the spectral density at energies close to the inelastic mode. In the strong coupling limit, a local negative $U…
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 …
We study rectangular graphene flakes using mean field states as the basis for a configuration interaction calculation, which allows us to analyze the low lying electronic excited states including electron correlations beyond the mean field level. We find that the lowest energy transition is polarized along the long axis of the flake, but the charge distributions involved in these transitions are invariably localized on the zigzag edges. We also investigate the impact of both short and long range impurity potentials on the optical properties of these systems. We predict that even a weak impurit…
