Bruno Uchoa

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.

Superconducting States of Pure and Doped Graphene

We study the superconducting phases of the two-dimensional honeycomb lattice of graphene. We find two spin singlet pairing states; s wave and an exotic p+ip that is possible because of the special structure of the honeycomb lattice. At half filling, the p+ip phase is gapless and superconductivity is a hidden order. We discuss the possibility of a superconducting state in metal coated graphene.

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.

Tailoring graphene with metals on top

We study the effects of metallic doping on the electronic properties of graphene using density functional theory in the local density approximation in the presence of a local charging energy. The electronic properties are sensitive to whether graphene is doped with alkali or transition metals. We estimate the charge transfer from a single layer of potassium on top of graphene in terms of the local charging energy of the graphene sheet. The coating of graphene with a nonmagnetic layer of palladium, on the other hand, can lead to a magnetic instability in coated graphene due to the hybridization between the transition metal and the carbon orbitals.

Zero-energy modes and gate-tunable gap in graphene on hexagonal boron nitride

In this article, we derive an effective theory of graphene on a hexagonal boron nitride (h-BN) substrate. We show that the h-BN substrate generically opens a spectral gap in graphene despite the lattice mismatch. The origin of that gap is particularly intuitive in the regime of strong coupling between graphene and its substrate, when the low-energy physics is determined by the topology of a network of zero-energy modes. For twisted graphene bilayers, where inversion symmetry is present, this network percolates through the system and the spectrum is gapless. The breaking of that symmetry by h-BN causes the zero-energy modes to close into rings. The eigenstates of these rings hybridize into flat bands with gaps in between. The size of this band gap can be tuned by a gate voltage and it can reach the order of magnitude needed to confine electrons at room temperature.

Transport through Andreev bound states in a graphene quantum dot

Gate-tunable Andreev bound states that arise within quantum dots formed beneath superconducting contacts deposited on a graphene sheet could be useful in the development of solid-state qubits.

The Effective Fine-Structure Constant of Freestanding Graphene Measured in Graphite

Weakly Interacting Graphene Many unusual properties of graphene are a consequence of the Dirac dispersion of its electrons—a linear relationship between an electrons momentum and energy. Naïvely, this dispersion leads to the conclusion that electrons in graphene are strongly affected by mutual electrostatic interactions; however, there is little experimental evidence for strong interaction. Reed et al. (p. 805) resolved this discrepancy by using inelastic x-ray scattering spectra of graphite (which consists of loosely bound layers of graphene) to estimate how much the electric field was damped by the presence of mobile charge carriers. In fact, damping was strong at distances in excess of 1 nanometer, suggesting that graphene is more weakly interacting than was assumed. Spectral analysis of graphite reveals an unexpectedly low influence of electron interactions in graphene. Electrons in graphene behave like Dirac fermions, permitting phenomena from high-energy physics to be studied in a solid-state setting. A key question is whether or not these fermions are critically influenced by Coulomb correlations. We performed inelastic x-ray scattering experiments on crystals of graphite and applied reconstruction algorithms to image the dynamical screening of charge in a freestanding graphene sheet. We found that the polarizability of the Dirac fermions is amplified by excitonic effects, improving screening of interactions between quasiparticles. The strength of interactions is characterized by a scale-dependent, effective fine-structure constant, αg*(k,ω), the value of which approaches 0.14±0.092~1/7 at low energy and large distances. This value is substantially smaller than the nominal αg=2.2, suggesting that, on the whole, graphene is more weakly interacting than previously believed.

Kondo quantum criticality of magnetic adatoms in graphene.

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 TK∝|J-Jc|1/3 near the critical coupling Jc, and the local spin is effectively screened by a super-Ohmic bath. For this class, the RKKY interaction decays spatially with a fast power law ∼1/R7. Away from half filling, we show that the exchange coupling in graphene can be controlled across the quantum critical region by gating. We propose that the vicinity of the Kondo quantum critical point can be directly accessed with scanning tunneling probes and gating.

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.