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 polarized bulk currents and a large magnetoresistance. In gated graphene the impurity spin is Kondo screened at low temperatures. However, at temperatures larger than the Kondo temperature, the anomalous magnetotransport properties are recovered.
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.
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…
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 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…
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 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…
The indirect Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling between on-site magnetic impurities is studied for two kinds of graphene nanoflakes consisting of approximately 100 carbon atoms, posessing either zigzag or armchair edge. The tight-binding Hamiltonian with Hubbard term is used in non-perturbative calculations of coupling between the impurities placed at the edge of the structure. In general, for zigzag-edged nanoflakes a pronounced coupling robust against charge doping is found, while for armchair-edged structures the interaction is weaker and much more sensitive to charge doping. Als…
We build symmetry adapted maximally localized Wannier states, and construct the low energy tight binding model for the four narrow bands of the twisted bilayer graphene. We do so when the twist angle is commensurate, near the `magic' value, and the narrow bands are separated from the rest of the bands by energy gaps. On each layer and sublattice, every Wannier state has three peaks near the triangular Moire lattice sites. However, each Wannier state is localized and centered around a site of the honeycomb lattice that is dual to the triangular Moire lattice. Space group and the time reversal s…
We examine the conditions necessary for the presence of localized magnetic moments on adatoms with inner shell electrons in graphene. We show that the low density of states at the Dirac point, and the anomalous broadening of the adatom electronic level,lead to the formation of magnetic moments for arbitrarily small local charging energy. As a result, we obtain an anomalous scaling of the boundary separating magnetic and non-magnetic states. We show that, unlike any other material, the formation of magnetic moments can be controlled by an electric field effect.
The indirect, charge-carrier mediated coupling between localized magnetic moments is studied for graphene nanoflakes of triangular shape and zig-zag edge. The characteristic feature of such nanoflakes is the presence of a shell of zero-energy states in the electronic spectrum. The tight-binding Hamiltonian supplemented with a Hubbard term is used for electronic structure calculations. The indirect RKKY (Ruderman-Kittel-Kasuya-Yosida) coupling energy is derived from the total electronic energy of the system in a non-perturbative way. The attention is focused on the on-site and plaquette impurit…
We consider the electronic structure near vacancies in the half-filled honeycomb lattice. It is shown that vacancies induce the formation of localized states. When particle-hole symmetry is broken, localized states become resonances close to the Fermi level. We also study the problem of a finite density of vacancies, obtaining the electronic density of states, and discussing the issue of electronic localization in these systems. Our results also have relevance for the problem of disorder in d-wave superconductors.
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…
We address the effective tight-binding Hamiltonian that describes the insulating Mott state of twisted graphene bilayers at a magic angle. In that configuration, twisted bilayers form a honeycomb superlattice of localized states, characterized by the appearance of flat bands with four-fold degeneracy. After calculating the maximally localized superlattice Wannier wavefunctions, we derive the effective spin model that describes the Mott state. We suggest that the system is an exotic ferromagnetic Mott insulator, with well defined experimental signatures.
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…
Kane and Mele predicted that in presence of spin-orbit interaction graphene realizes the quantum spin Hall state. However, exceptionally weak intrinsic spin-orbit splitting in graphene ($\approx 10^{-5}$ eV) inhibits experimental observation of this topological insulating phase. To circumvent this problem, we propose a novel approach towards controlling spin-orbit interactions in graphene by means of covalent functionalization of graphene edges with functional groups containing heavy elements. Proof-of-concept first-principles calculations show that very strong spin-orbit coupling can be induc…
We study the low energy properties of warped monolayer graphene, where the symmetry of the original honeycomb lattice reveals itself. The zero energy solutions are Majorana fermions, whose wavefunction, originating from the corresponding modified Dirac equation is spatially localized. Experimental consequences are discussed.
We employ the exact eigenstate basis formalism to study electrical conductivity in graphene, in the presence of short-range diagonal disorder and inter-valley scattering. We find that for disorder strength, $W \ge$ 5, the density of states is flat. We, then, make connection, using the MRG approach, with the work of Abrahams \textit{et al.} and find a very good agreement for disorder strength, $W$ = 5. For low disorder strength, $W$ = 2, we plot the energy-resolved current matrix elements squared for different locations of the Fermi energy from the band centre. We find that the states close to …
We investigate magnetic instabilities in charge-neutral twisted bilayer graphene close to so-called "magic angles" using a combination of real-space Hartree-Fock and dynamical mean-field theories. In view of the large size of the unit cell close to magic angles, we examine a previously proposed rescaling that permits to mimic the same underlying flat minibands at larger twist angles. We find that localized magnetic states emerge for values of the Coulomb interaction $U$ that are significantly smaller than what would be required to render an isolated layer antiferromagnetic. However, this effec…
A theory of spin relaxation in graphene including intrinsic, Bychkov-Rashba, and ripple spin-orbit coupling is presented. We find from spin relaxation data by Tombros et al. [Nature 448, 571 (2007).] that intrinsic spin-orbit coupling dominates over other contributions with a coupling constant of 3.7 meV. Although it is 1-3 orders of magnitude larger than those obtained from first principles, we show that comparable values are found for other honeycomb systems, MgB2 and LiC6; the latter is studied herein by electron spin resonance (ESR). We predict that spin coherence is longer preserved for s…
We use the regularized kernel polynomial method (RKPM) to numerically study the effect disorder on a single layer of graphene. This accurate numerical method enables us to study very large lattices with millions of sites, and hence is almost free of finite size errors. Within this approach, both weak and strong disorder regimes are handled on the same footing. We study the tight-binding model with on-site disorder, on the honeycomb lattice. We find that in the weak disorder regime, the Dirac fermions remain extended and their velocities decrease as the disorder strength is increased. However, …
