Valeri N. Kotov

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.

Localized Magnetic States in Graphene

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 nonmagnetic states. We show that, unlike any other material, the formation of magnetic moments can be controlled by an electric field effect.

Collective singlet excitations and evolution of raman spectral weights in the 2D spin dimer compound SrCu2(BO3)(2)

Raman light scattering of the two-dimensional quantum spin system SrCu2(BO3)(2) shows a rich structure in the magnetic excitation spectrum, including several well-defined bound state modes at low temperature, and a scattering continuum and quasielastic light scattering contributions at high temperature. The key to the understanding of the unique features of SrCu2(BO3)(2) is the presence of strong interactions between well-localized triplet excitations in the network of orthogonal spin dimers realized in this compound.

Supercritical Coulomb impurities in gapped graphene

testing 12,13,15 . We show here that this analogy achieves its fullest in gapped graphene, where one can resolve the incremental charging of the vacuum, with strong implications for the screening of the Coulomb center. The rest of the paper is organized as follows. In Sec. II we introduce our model, and in Sec. III its properties in the massless limit are reviewed. In Sec. IV the behavior of discrete energy levels in the massive case is discussed. We examine in detail the structure of the critical wavefunction and the corresponding renormalization of the critical Coulomb coupling in Sec. V. In Sec. VI we study the behavior of the vacuum charge across the critical point. Sec. VII contains the corresponding results for a finite-size system (where the energy gap is due to the finite size only). Sec. VIII contains a discussion of our results and conclusions.

Adatoms in graphene

We review the problem of adatoms in graphene under two complementary points of view, scattering theory and strong correlations. We show that in both cases impurity atoms on the graphene surface present effects that are absent in the physics of impurities in ordinary metals. We discuss how to observe these unusual effects with standard experimental probes such as scanning tunneling microscopes, and spin susceptibility.

Polarization charge distribution in gapped graphene : Perturbation theory and exact diagonalization analysis

We study the distribution of vacuum polarization charge induced by a Coulomb impurity in massive graphene. By analytically computing the polarization function, we show that the charge density is distributed in space in a non-trivial fashion, and on a characteristic length-scale set by the effective Compton wavelength. The density crosses over from a logarithmic behavior below this scale, to a power law variation above it. Our results in the continuum limit are confirmed by explicit diagonalization of the corresponding tight-binding model on a finite-size lattice. Electron-electron interaction effects are also discussed.

Electron-electron interactions in the vacuum polarization of graphene

We discuss the effect of electron-electron interactions on the static polarization properties of graphene beyond RPA. Divergent self-energy corrections are naturally absorbed into the renormalized coupling constant

Effect of uniaxial strain on ferromagnetic instability and formation of localized magnetic states on adatoms in graphene

\alpha

Van der Waals forces and electron-electron interactions in two strained graphene layers

. We find that the lowest order vertex correction, which is the first non-trivial correlation contribution, is finite, and about 30% of the RPA result at strong coupling

Weak antiferromagnetism and dimer order in quantum systems of coupled tetrahedra

\alpha \sim 1