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 renormalization parameter that shifts the impurity level is insufficient to invert the sign of the energy level. Consequently, the state at half-filling is stable unless a gate voltage is tuned such that the Fermi level touches the edge of the broadened impurity level. Only in this case the zero field susceptibility is finite and shows a pronounced peak structure with the gate voltage.
We examine theoretically the signatures of magnetic adatoms in graphene probed by scanning tunneling spectroscopy (STS). When the adatom hybridizes equally with the two graphene sublattices, the broadening of the local adatom level is anomalous and can scale with the cube of the energy. In contrast to ordinary metal surfaces, the adatom local moment can be suppressed by the proximity of the probing scanning tip. We propose that the dependence of the tunneling conductance on the distance between the tip and the adatom can provide a clear signature for the presence of local magnetic moments. We …
It is generally believed that free-standing graphene does not demonstrate any ferroic properties. In the present work we revise this statement and show that single graphene sheet with a pair of magnetic adatoms can be driven into ferroelectric (FE) and multiferroic (MF) phases by tuning the Dirac cones slope. The transition into the FE phase occurs gradually, but an anomalous MF phase appears abruptly by means of a Quantum Phase Transition. Our findings suggest that such features should exist in graphene recently investigated by Scanning Tunneling Microscopy (Science 352, 437 (2016)).
By applying tight binding model of adatoms in graphene, we study theoretically the localized aspects of the interaction between transition metal atoms and graphene. Considering the electron-electron interaction by adding a Hubbard term in the mean-field approximation, we find the spin-polarized localized and total density of states. We obtain the coupled system of equations for the occupation number for each spin in the impurity and we study the fixed points of the solutions. By comparing the top site and hollow site adsorption, we show that the anomalous broadening of the latter allows to obt…
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 …
The electronic structure of selected rare-earth atoms adsorbed on a free-standing graphene was investigated using methods beyond the conventional density functional theory (DFT+U, DFT+HIA and DFT+ED). The influence of the electron correlations and the spin-orbit coupling on the magnetic properties has been examined. The DFT+U method predicts both atoms to carry local magnetic moments (spin and orbital) contrary to a nonmagnetic $f^6$ ($J=0$) ground-state configuration of Sm in the gas phase. Application of DFT${}+{}$Hubbard-I (HIA) and DFT${}+{}$exact diagonalization (ED) methods cures this pr…
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…
We study magnetism of an adatom adsorbed on AA-stacked bilayer graphene (BLG) in both unbiased and biased cases, using the Anderson impurity model. We find different magnetic phase diagrams for the adatom, depending on the energy level of the adatom, which varies from the magnetic phase diagram of adatom in normal metals to that in graphene. This is due to the individual energy dependence of the density of states (DOS) of AA-stacked BLG and anomalous broadening of the adatom energy level. Furthermore we investigate the effect of a bias voltage on DOS of AA-stacked and show that the magnetizati…
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…
We present a theoretical study of the optical conductivity of graphene with magnetic and nonmagnetic adatoms. First, by introducing alternating potential in a pure graphene, we demonstrate a gap formation in the density of states and the corresponding optical conductivity. We highlight the distinction between such a gap formation and the so-called Pauli blocking effect. Next, we apply this idea to graphene with adatoms by introducing magnetic interactions between the carrier spins and the spins of the adatoms. Exploring various possible ground-state spin configurations of the adatoms, we find …
We discuss theoretically the local density of states (LDOS) of a graphene sheet hosting two distant adatoms located at the center of the hexagonal cells. By putting laterally a Scanning Tunneling Microscope (STM) tip over a carbon atom, two remarkable novel effects can be detected: i) a multilevel structure in the LDOS and ii) beating patterns in the induced LDOS. We show that both phenomena occur nearby the Dirac points and are highly anisotropic. Furthermore, we propose conductance experiments employing STM as a probe for the observation of such exotic manifestations in the LDOS of graphene …
We use first-principles Quantum Monte-Carlo simulations to study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between hydrogen adatoms attached to a graphene sheet. We find that the pairwise RKKY interactions at distances of a few lattice spacings are strongly affected by inter-electron interactions, in particular, the potential barrier between widely separated adatoms and the dimer configuration becomes wider and thus harder to penetrate. We also point out that anti-ferrromagnetic and charge density wave orderings have very different effects on the RKKY interaction. Finally, we analyz…
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 electronic properties of graphene with finite concentration of vacancies or other resonant scatterers by a straightforward lattice Quantum Monte Carlo calculations. Taking into account realistic long-range Coulomb interaction we calculate distribution of spin density associated to midgap states and demonstrate antiferromagnetic ordering. Energy gaps are open due to the interaction effects, both in the bare graphene spectrum and in the vacancy/impurity bands. In the case of 5 % concentration of resonant scatterers the latter gap is estimated as 0.7 eV and 1.1 eV for graphene on boron n…
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…
We perform Monte Carlo simulations to study the interplay of structural and magnetic order in single layer graphene covered with magnetic adatoms. We propose that the presence of ripples in the graphene structure can lead to clustering of the adatoms and to a variety of magnetic states such as super-paramagnetism, antiferromagnetism, ferromagnetism and spin glass behavior. We derive the magnetization hysteresis and also the magnetoresistance curves in the variable range hopping regime, which can provide experimental signatures for ripple induced clustering and magnetism. We propose that the ma…
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…
We investigate the effect of an applied uniaxial strain on the ferromagnetic instability due to long- range Coulomb interaction between Dirac fermions in graphene. In case of undeformed graphene the ferromagnetic exchange instability occurs at sufficiently strong interaction within the Hartree- Fock approximation. In this work we show that using the same theoretical framework but with an additional applied uniaxial strain, the transition can occur for much weaker interaction, within the range in suspended graphene. We also study the consequence of strain on the formation of localized magnetic …
The phase diagram of graphene decorated with magnetic adatoms distributed either on a single sublattice, or evenly over the two sublattices, is computed for adatom concentrations as low as $\sim1\%$. Within the framework of the $s$-$d$ interaction, we take into account disorder effects due to the random positioning of the adatoms and/or to the thermal fluctuations in the direction of magnetic moments. Despite the presence of disorder, the magnetic phases are shown to be stable down to the lowest concentration accessed here. This result agrees with several experimental observations where adatom…
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 address the interaction of graphene with 3d transition metal adatoms and the formation of localized magnetic moments by means of first-principles calculations. By comparing calculations within the generalized gradient approximation (GGA) to GGA+U we find that the electronic configuration and the adsorption geometries can be very sensitive to effects of local Coulomb interactions U in the transition metal d-orbitals. We find high-spin configurations being favorable for Cr and Mn adatoms independent of the functional. For Fe, Co and Ni different electronic configurations are realized dependin…
We explore theoretically the formation of bound states in the continuum (BICs) in graphene hosting two collinear adatoms situated at different sides of the sheet and at the center of the hexagonal cell, where a phantom atom of a fictitious lattice emulates the six carbons of the cell. We verify that in this configuration the local density of states (LDOS) near the Dirac points exhibits two characteristic features: i) the cubic dependence on energy instead of the linear one for graphene as found in New J. Phys. 16, 013045 (2014) and ii) formation of BICs as aftermath of a Fano destructive inter…
We show within a local self-consistent mean-field treatment that a random distribution of magnetic adatoms can open a robust gap in the electronic spectrum of graphene. The electronic gap results from the interplay between the nature of the graphene sublattice structure and the exchange interaction between adatoms.The size of the gap depends on the strength of the exchange interaction between carriers and localized spins and can be controlled by both temperature and external magnetic field. Furthermore, we show that an external magnetic field creates an imbalance of spin-up and spin-down carri…
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…
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…
Graphene hosting a pair of collinear adatoms in the phantom atom configuration has pseudogap with cubic scaling on energy, $Δ\propto|\varepsilon|^{3}$ which leads to the appearance of spin-degenerate bound states in the continuum (BICs) [Phys. Rev. B 92, 045409 (2015)]. In the case when adatoms are locally coupled to a single carbon atom the pseudogap scales linearly with energy, which prevents the formation of BICs. In this Letter, we explore the effects of non-local coupling characterized by the Fano factor of interference $q_{0},$ tunable by changing the slope of the Dirac cones in the grap…
We use quantum Monte Carlo method to study the indirect coupling between two magnetic impurities on the zigzag edge of graphene ribbon, with respect to the chemical potential $μ$. We find that the spin-spin correlation between two adatoms located on the nearest sites in the zigzag edge are drastically suppressed around the zero-energy. As we switch the system away from half-filling, the antiferromagnetic correlation is first enhanced and then decreased. If the two adatoms are adsorbed on the sites belonging to the same sublattice, we find similar behavior of spin-spin correlation except for a …
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…
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…
