Session L11: Focus Session: Graphene Structure, Stacking, Interactions: Magnetism and Interactions

Kondo Effect in Bilayer Graphene

Because of the linear dependence of the density of states (near Dirac points), the physics of localized magnetic moments on graphene exhibits unique characteristics [1]. From the experiments by Mattos et al [2], where a possible observation of the 2-channel Kondo effect was reported, to recent studies on vacancies [3], the role of local moments on graphene remains poorly understood. The technical difficulties to determine the nature of the origin of the local moment add to the complexity of the problem. To gain insight into this problem, we have undertaken a study of a bilayer graphene system with Bernal stacking and an intercalated magnetic impurity. We model the system with a multiband Anderson impurity model and obtain the effective Kondo Hamiltonian via a Schrieffer-Wolff transformation. Although several conducting channels couple to the impurity, the standard 1-channel Kondo regime is recovered at low temperatures. The effective Kondo exchange couplings depend on the interlayer hopping giving rise to tunable Kondo temperatures. \\[4pt] [1] P. S. Cornglia et al., PRL 102, 046801 (2009); B. Uchoa et al., PRL 106, 016801 (2011)\\[0pt] [2] L. Mattos et al. (unpublished)\\[0pt] [3] J. -H. Chen et al., Nature Phys. 7, 535(2011); M. M. Ugeda et al., PRL 104, 096804 (2010).   

Mid-gap states and Kondo effect in disordered graphene

Recent experiments on graphene flakes with short range scattering defects have stengthen the interest on Kondo physics in graphene systems. The experimental data show a temperature dependence of the resistivity consistent with the low-temperature Kondo screening of local magnetic moments. While the linear dispersion in the density of states in graphene justify a pseudogap Kondo model showing a rich variety of quantum critical behavior as a function of the gate-controlled chemical potential, the presence of disorder can alter this effect in favor of the ``standard'' Kondo model, with a Fermi-liquid ground state. We study these effects with different numerical methods. Tight-binding calculations for diluted scattering defects show the appearance of quasi-localized midgap states in the local density of states at the vicinity of the charge neutrality point. This leads to the formulation a Anderson-like model of localized states within the graphene matrix, which may lead to a Kondo screening consistent with the experiments. To verify this hypothesis, we perform numerical renormalization group (NRG) calculations to study the gate-dependence of the Kondo temperature and the transport properties of this model.   

Dynamic RKKY interaction in graphene

The growing interest in carbon-based spintronics has stimulated a number of recent theoretical studies on the RKKY interaction in graphene, based on which the energetically favourable alignment between magnetic moments embedded in this material can be calculated. The general consensus is that the strength of the RKKY interaction in graphene decays as $1/D^3$ or faster, where $D$ is the separation between magnetic moments. Such an unusually fast decay for a 2-dimensional system suggests that the RKKY interaction may be too short ranged to be experimentally observed in graphene. Here we show in a mathematically transparent form that a far more long ranged interaction arises when the magnetic moments are taken out of their equilibrium positions and set in motion. We not only show that this dynamic version of the RKKY interaction in graphene decays far more slowly but also propose how it can be observed with currently available experimental methods.   

Formation of Localized Magnetic States on Adatoms in Uniaxially Strained Graphene

We investigate the effect of applied uniaxial strain on the formation of localized magnetic states on adatoms in graphene. In the framework of the single impurity Anderson model, we systematically analyze the interplay between the anisotropic (strain-induced) nature of the Dirac fermions and the on-site Hubbard interaction. We numerically calculate the polarization of the electrons in the localized orbital within the mean-field self-consistent scheme. A phase diagram is obtained, containing non-magnetic as well as large magnetic regions, which can find prospective applications in the field of carbon-based spintronics.   

Spin and band ferromagnetism in trilayer graphene

We study the ground state properties of an ABA-stacked trilayer graphene. The low energy band structure can be described by a combination of both a linear and a quadratic particle-hole symmetric dispersion, reminiscent of monolayer- and bilayer-graphene, respectively. The multi-band structure offers more channels for instability towards ferromagnetism when the Coulomb interaction is taken into account. Indeed, if one associates a subband-index degree of freedom to the bands (parabolic/linear), it is possible to realize also a band-ferromagnetic state, where there is a shift in the energy bands, since they fill up differently. By using a variational procedure, we compute the exchange energies for all possible variational ground states and identify the parameter space for the occurrence of spin- and band-ferromagnetic instabilities as a function of doping and interaction strength.   

Magnetic order in graphene with broken inversion symmetry

We study the effect of sublattice symmetry breaking on the magnetic and transport properties of two dimensional graphene as well as zigzag terminated one dimensional graphene nanostructures. The systems are described with the Hubbard model within the collinear mean field approximation. In the case of 2D and zigzag ribbons we compute the phase diagram, at half-filling, defined by the normalized interaction strength U/t and the sublattice potential V/t, where t is the first neighbor hopping. In the case of 2D graphene we find that the system is always insulating, except at the transition between the antiferromagnetic (AF) and the non-magnetic (NM) phase where the system is half-metallic. In the case of zigzag ribbons, at finite V we find that the system undergoes a phase transition from non-magnetic insulator for U$<$Uc (V) to a phase with ferromagnetic order in the edges and antiferromagnetic inter-edge coupling. The conduction properties of the magnetic phase depend on V and can be insulating, conducting and even half-metallic, yet the total magnetic moment in the system is zero. In the latter case, we find a strong spin filter effect.   

Magnetic Properties of Rhombohedral Graphene Thin Films

Ever since the fabrication of single and few layers graphene, the graphene thin films have been attracting so much attention in the field not only of low-dimensional sciences but also of nano-scale technologies due to their perfect two-dimensional network. One of fascinating issues in this carbon allotrope is the intrinsic magnetism that is inherent in their topological properties. We have demonstrated that the (0001) surfaces of graphene thin film with rhombohedral-stacked arrangement exhibit ferrimagnetic spin ordering induced by flat dispersion band associated with the peculiar surface localized electron states classified as the ``edge state'' [1]. In this work, we systematically investigate how the electronic and magnetic properties of the rhombohedral-stacked graphene thin films depend on the number of graphene layers, BN substrate, and uniaxial pressure using first-principles total-energy calculations in the framework of density functional theory [2]. \\[4pt] [1] M. Otani, M. Koshino, Y. Takagi, and S. Okada, Phys. Rev. B 81 (2010) 161403(R). \\[0pt] [2] N. T. Cuong, M. Otani, and S. Okada, Surf. Sci. (2011), doi:10.1016/j.susc.2011.10.001   

Emergence of atypical magnetic and electronic properties in graphitic nanowiggles

Graphitic nanowiggles (GNWs) are periodic repetitions of non-aligned finite-sized graphitic nanoribbon domains seamlessly stitched together without structural defects. These complex nanostructures have been recently fabricated using the self-assembly and subsequent fusion of small aromatic compound (Nature \textbf{466}, 470 (2010)). The structures are predicted to possess unusual properties, such as tunable bandgaps and versatile magnetic behaviors (Phys. Rev. Lett. \textbf{107}, 135501 (2011)). First-principles theory was used to highlight the microscopic origin of the emerging electronic and magnetic properties of the main subclasses of GNWs, thereby establishing a road-map for guiding the design and synthesis of specific GNWs with targeted nanoelectronic, optoelectronic, and spintronic properties. We will show the unusual versatility of GNWs' magnetic properties, we will highlight the variation of electronic properties with the details of the structures and how these structures can be used to transport electrons.   

Chiral superconductivity from repulsive interactions in doped graphene

We present a model wherein repulsive interactions unambiguously lead to superconductivity with enhanced Tc. The superconducting state is the chiral d + id superconducting state, which has no known experimental realizations. Intriguingly, our model has a natural realization in graphene that is doped to the M point of the Brilliouin zone. At this doping level, the Fermi surface nesting and the divergent density of states can produce interaction driven instabilities to exotic phases with high energy scales. Analyzing the competition between various ordering tendencies within a renormalisation group framework, we find that the leading instability is to d-wave superconductivity, for any choice of weak repulsive interactions. The instability develops simultaneously in two distinct d-wave channels, which are degenerate by lattice symmetries. Analysis of the pairing below Tc reveals that both orders co-exist to produce d + id superconductivity, with the phase of the order parameter winding by $4\pi$ as we go around the Fermi surface.   

Competing many-body instabilities and unconventional superconductivity in graphene

The band structure of graphene exhibits van Hove singularities (VHS) at doping x = $\pm$1/8 away from the Dirac point. Near the VHS, interactions effects, enhanced due to the large density of states, can give rise to various many-body phases at experimentally accessible temperatures. We study the competition between different many-body instabilities in graphene using functional renormalization group (FRG). We predict a rich phase diagram, which, depending on long range hopping as well as screening strength and absolute scale of the Coulomb interaction, contains a d + id-wave superconducting (SC) phase, or a spin density wave phase at the VHS. The d + id state is expected to exhibit quantized charge and spin Hall response, as well as Majorana modes bound to vortices. In the vicinity of the VHS, we find singlet d + id-wave as well as triplet f -wave SC phases. \\[4pt] [1] arXiv:1109.2953v1   

Power law Kohn anomaly in graphene induced by Coulomb interactions

Phonon dispersions generically display non-analytic points, known as Kohn anomalies, due to electron-phonon interactions. We analyze this phenomenon for a zone boundary phonon in graphene. When electron-electron interactions with coupling constant $\beta$ are taken into account, one observes behavior demonstrating that the electrons are in a critical phase: the phonon dispersion and lifetime develop power law behavior with $\beta$ dependent exponents. The observation of this signature would allow experimental access to the critical properties of the electron state, and would provide a measure of its proximity to an excitonic insulating phase.   

Effect of electron-phonon coupling on energy and density of states renormalizations of dynamically screened graphene

Motivated by recent tunneling and angle-resolved photoemission (ARPES) work [1,2], we explore the combined effect of electron-electron and electron-phonon couplings on the renormalized energy dispersion, the spectral function, and the density of states of doped graphene. We find that the plasmarons seen in ARPES are also observable in the density of states and appear as structures with quadratic dependence on energy about the minima. Further, we illustrate how knowledge of the slopes of both the density of states and the renormalized dispersion near the Fermi level can allow for the separation of momentum and frequency dependent renormalizations to the Fermi velocity. This analysis should allow for the isolation of the renormalization due to the electron-phonon interaction from that of the electron-electron interaction. \\[4pt] [1] Brar et al. Phys. Rev. Lett. 104, 036805 (2010) [2] Bostwick et al. Science 328, p.999 (2010)   

Screening and electrostatic doping in multilayer graphene systems

We study the electrostatic screening in multilayer graphene systems using ab initio calculations and analytical models. First principles calculations reveal that oriented (Bernal) and turbostratic graphene multilayers in contact with a metal slab show only small differences in their charge distribution despite their dissimilar electronic structure. In the turbostratic systems the layer decoupling enables the identification of the Dirac point for each individual layer. We then measure the shift of each Dirac point relative to the Fermi level of the system and compute the charge transfer to each layer. Results are compared with an analytical model considering discrete layers. The model shows that at T = 0 charge screening is highly nonlinear due to the vanishing density of states at the Fermi level. More importantly a strong dependence on charge and temperature results in a change of the screening length by more than an order of magnitude depending on the experimental conditions, reconciling the large range of screening lengths previously reported in experiments.   

Screening in Chiral Multilayer Graphene

We calculate the static polarization function of multilayer graphene and study the effects of stacking arrangement, carrier density and onsite energy difference. At low densities, the energy spectrum of multilayer graphene is described by a set of chiral two-dimensional electron systems and the associated chiral nature determines the screening properties of multilayer graphene showing very different behavior depending on whether chirality indices are even or odd. As the density increases, the energy spectrum follows that of monolayer graphene thus the polarization function approaches that of monolayer graphene.   

Unusual electron self-energy in graphene

Electron-Electron interactions bear important information on fundamental electronic properties such as electron effective mass, conductivity, and charge mobility. By using angle-resolved photoemission spectroscopy, we study unusual electron self-energy in graphene induced by the electron-electron interactions, which are distinguished from those of an ordinary Fermi liquid. Our findings provide a new route for two-dimensional electron systems toward device applications.