Orbital symmetry fingerprints for magnetic adatoms in graphene

In this paper, we describe the formation of local resonances in graphene in the presence of magnetic adatoms containing localized orbitals of arbitrary symmetry, corresponding to any given angular momentum state. We show that quantum interference effects which are naturally inbuilt in the honeycomb lattice in combination with the specific orbital symmetry of the localized state lead to the formation of fingerprints in differential conductance curves. In the presence of Jahn-Teller distortion effects, which lift the orbital degeneracy of the adatoms, the orbital symmetries can lead to distinctive signatures in the local density of states. We show that those effects allow scanning tunneling probes to characterize adatoms and defects in graphene.Comment: 15 pages, 11 figures. Added discussion about the multi-orbital case and the validity of the single orbital picture. Published versio

Theory of Scanning Tunneling Spectroscopy of Magnetic Adatoms in Graphene

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 also show that tunneling conductance can distinguish whether the adatom is located on top of a carbon atom or in the center of a honeycomb hexagon.Comment: 4.1 pages, 4 figure

Theoretical Aspects of the Fractional Quantum Hall Effect in Graphene

We review the theoretical basis and understanding of electronic interactions in graphene Landau levels, in the limit of strong correlations. This limit occurs when inter-Landau-level excitations may be omitted because they belong to a high-energy sector, whereas the low-energy excitations only involve the same level, such that the kinetic energy (of the Landau level) is an unimportant constant. Two prominent effects emerge in this limit of strong electronic correlations: generalised quantum Hall ferromagnetic states that profit from the approximate four-fold spin-valley degeneracy of graphene's Landau levels and the fractional quantum Hall effect. Here, we discuss these effects in the framework of an SU(4)-symmetric theory, in comparison with available experimental observations.Comment: 12 pages, 3 figures; review for the proceedings of the Nobel Symposium on Graphene and Quantum Matte

Magnetic structure and critical behavior of GdRhIn5_{5}: resonant x-ray diffraction and renormalization group analysis

The magnetic structure and fluctuations of tetragonal GdRhIn5 were studied by resonant x-ray diffraction at the Gd LII and LIII edges, followed by a renormalization group analysis for this and other related Gd-based compounds, namely Gd2IrIn8 and GdIn3. These compounds are spin-only analogs of the isostructural Ce-based heavy-fermion superconductors. The ground state of GdRhIn5 shows a commensurate antiferromagnetic spin structure with propagation vector tau = (0,1/2, 1/2), corresponding to a parallel spin alignment along the a-direction and antiparallel alignment along b and c. A comparison between this magnetic structure and those of other members of the Rm(Co,Rh,Ir)n In3m+2n family (R =rare earth, n = 0, 1; m = 1, 2) indicates that, in general, tau is determined by a competition between first-(J1) and second-neighbor(J2) antiferromagnetic (AFM) interactions. While a large J1 /J2 ratio favors an antiparallel alignment along the three directions (the so-called G-AFM structure), a smaller ratio favors the magnetic structure of GdRhIn5 (C-AFM). In particular, it is inferred that the heavy-fermion superconductor CeRhIn5 is in a frontier between these two ground states, which may explain its non-collinear spiral magnetic structure. The critical behavior of GdRhIn5 close to the paramagnetic transition at TN = 39 K was also studied in detail. A typical second-order transition with the ordered magnetization critical parameter beta = 0.35 was experimentally found, and theoretically investigated by means of a renormalization group analysis.Comment: 22 pages, 4 figure

Surface superconductivity in multilayered rhombohedral graphene: Supercurrent

The supercurrent for the surface superconductivity of a flat-band multilayered rhombohedral graphene is calculated. Despite the absence of dispersion of the excitation spectrum, the supercurrent is finite. The critical current is proportional to the zero-temperature superconducting gap, i.e., to the superconducting critical temperature and to the size of the flat band in the momentum space

Nodal liquid and s-wave superconductivity in transition metal dichalcogenides

We explore the physical properties of a unified microscopic theory for the coexistence of superconductivity and charge density waves in two-dimensional transition metal dichalcogenides. In the case of particle-hole symmetry the elementary particles are Dirac fermions at the nodes of the charge density wave gap. When particle-hole symmetry is broken electron (hole) pockets are formed around the Fermi surface. The superconducting ground state emerges from the pairing of nodal quasi-particles mediated by acoustic phonons via a piezoelectric coupling. We calculate several properties in the s-wave superconducting phase, including specific heat, ultra-sound absorption, nuclear magnetic relaxation, thermal, and optical conductivities. In the case with particle-hole symmetry, the specific heat jump at the transition deviates strongly from ordinary superconductors. The nuclear magnetic response shows an anomalous anisotropy due to the broken time-reversal symmetry of the superconducting gap, induced by the triple charge density wave state. The loss of lattice inversion symmetry in the charge density wave phase leads to anomalous coherence factors in the optical conductivity and to the appearance of an absorption edge at the optical gap energy. Furthermore, optical and thermal conductivities display anomalous peaks in the infrared when particle-hole symmetry is broken.Comment: 23 pages, 16 figures. Published versio

The Physics of Kondo Impurities in Graphene

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 other quantum impurity problems, e.g., in unconventional superconductors, topological insulators, and quantum spin liquids.Comment: 27 pages, 8 figs. Review article prepared for Rep. Prog. Phys. ("key issues" section). (v2) Final version as publishe

Electron-Electron Interactions in Graphene: Current Status and Perspectives

We review the problem of electron-electron interactions in graphene. Starting from the screening of long range interactions in these systems, we discuss the existence of an emerging Dirac liquid of Lorentz invariant quasi-particles in the weak coupling regime, and strongly correlated electronic states in the strong coupling regime. We also analyze the analogy and connections between the many-body problem and the Coulomb impurity problem. The problem of the magnetic instability and Kondo effect of impurities and/or adatoms in graphene is also discussed in analogy with classical models of many-body effects in ordinary metals. We show that Lorentz invariance plays a fundamental role and leads to effects that span the whole spectrum, from the ultraviolet to the infrared. The effect of an emerging Lorentz invariance is also discussed in the context of finite size and edge effects as well as mesoscopic physics. We also briefly discuss the effects of strong magnetic fields in single layers and review some of the main aspects of the many-body problem in graphene bilayers. In addition to reviewing the fully understood aspects of the many-body problem in graphene, we show that a plethora of interesting issues remain open, both theoretically and experimentally, and that the field of graphene research is still exciting and vibrant.Comment: Review Article to appear in Reviews of Modern Physics. 62 pages, 44 figure

Properties of Graphene: A Theoretical Perspective

In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorist's perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of the quasiparticles near the Dirac point with a Landau level at zero energy. We address the unique integer quantum Hall effects, the role of electron correlations, and the recent observation of the fractional quantum Hall effect in the monolayer graphene. The quantum Hall effect in bilayer graphene is fundamentally different from that of a monolayer, reflecting the unique band structure of this system. The theory of transport in the absence of an external magnetic field is discussed in detail, along with the role of disorder studied in various theoretical models. We highlight the differences and similarities between monolayer and bilayer graphene, and focus on thermodynamic properties such as the compressibility, the plasmon spectra, the weak localization correction, quantum Hall effect, and optical properties. Confinement of electrons in graphene is nontrivial due to Klein tunneling. We review various theoretical and experimental studies of quantum confined structures made from graphene. The band structure of graphene nanoribbons and the role of the sublattice symmetry, edge geometry and the size of the nanoribbon on the electronic and magnetic properties are very active areas of research, and a detailed review of these topics is presented. Also, the effects of substrate interactions, adsorbed atoms, lattice defects and doping on the band structure of finite-sized graphene systems are discussed. We also include a brief description of graphane -- gapped material obtained from graphene by attaching hydrogen atoms to each carbon atom in the lattice.Comment: 189 pages. submitted in Advances in Physic

Spin-half paramagnetism in graphene induced by point defects

Using magnetization measurements, we show that point defects in graphene - fluorine adatoms and irradiation defects (vacancies) - carry magnetic moments with spin 1/2. Both types of defects lead to notable paramagnetism but no magnetic ordering could be detected down to liquid helium temperatures. The induced paramagnetism dominates graphene's low-temperature magnetic properties despite the fact that maximum response we could achieve was limited to one moment per approximately 1000 carbon atoms. This limitation is explained by clustering of adatoms and, for the case of vacancies, by losing graphene's structural stability.Comment: 14 pages, 14 figure