Abstract:
We have studied zigzag and armchair graphene nano ribbons (GNRs), described by the Hubbard Hamiltonian using quantum many body configuration interaction methods. Due to finite termination, we find that the bipartite nature of the graphene lattice gets destroyed at the edges making the ground state of the zigzag GNRs a high spin state, whereas the ground state of the armchair GNRs remains a singlet. Our calculations of charge and spin densities suggest that, although the electron density prefers to accumulate on the edges, instead of spin polarization, the up and down spins prefer to mix throughout the GNR lattice. While the many body charge gap results in insulating behavior for both kinds of GNRs, the conduction upon application of electric field is still possible through the edge channels because of their high electron density. Analysis of optical states suggest differences in quantum efficiency of luminescence for zigzag and armchair GNRs, which can be probed by simple experiments.

Abstract:
We theoretically study various aspects of the electron-surface optical phonon interaction effects in graphene on a substrate made of polar materials. We calculate the electron self-energy in the presence of the surface phonon-mediated electron-electron interaction focusing on how the linear chiral graphene dispersion is renormalized by the surface phonons. The electron self-energy as well as the quasiparticle spectral function in graphene are calculated, taking into account electron-polar optical phonon interaction by using a many body perturbative formalism. The scattering rate of free electrons due to polar interaction with surface optical phonons in a dielectric substrate is calculated as a function of the electron energy, temperatures, and carrier density. Effects of screening on the self-energy and scattering rate are discussed. Our theory provides a comprehensive quantitative (and qualitative) picture for surface phonon interaction induced many-body effects and hot electron relaxation in Dirac materials.

Abstract:
Influence of the chiral symmetry on the many-body problem in multilayer graphene in magnetic fields is investigated. For a spinless electron model on the honeycomb lattice the many-body ground state is shown to be a doubly-degenerate chiral condensate irrespective of the number of layers. The energy spectrum calculated numerically with the exact diagonalization method reveals for ABC-stacked multilayer graphenes that the many-body gap decreases monotonically with the number of layers.

Abstract:
We study a many-body ground state of graphene in perpendicular magnetic fields. Chiral symmetry in graphene enables us to determine the many-body ground state, which turns out to be a doubly degenerate chiral condensate for the half-filled (undoped) case. In the ground state a prominent charge accumulation emerges along zigzag edges. We also show that gapless excitations are absent despite the presence of the robust edge modes, which is consistent with the Chern number C = 0.

Abstract:
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.

Abstract:
Many-body electron-electron interaction effects are theoretically considered in monolayer graphene from a continuum effective field-theoretic perspective by going beyond the standard leading-order perturbative renormalization group (RG) analysis. Given that the bare fine structure constant in graphene is of order unity, which is neither small to justify a perturbative expansion nor large enough for strong-coupling theories to be applicable, the problem is a difficult one, with some similarity to 2+1-dimensional strong-coupling quantum electrodynamics (QED). In this work, we take a systematic and comprehensive analytical approach, working primarily at the Dirac point (intrinsic graphene), by going up to three loops in the diagrammatic expansion to both ascertain the validity of perturbation theory and to estimate quantitatively higher-order renormalization effects. While no direct signatures for non-Fermi liquid behavior at the Dirac point have yet been observed experimentally, there is ample evidence for the interaction-induced renormalization of the graphene velocity as the carrier density approaches zero. We provide a critical comparison between theory and experiment, using both bare- and screened-interaction (RPA) calculations. We find that while the one-loop RG analysis gives reasonable agreement with the experimental data, especially when screening and finite-density effects are included through the RPA, the two-loop analysis reveals a strong-coupling critical point in suspended graphene, signifying either a quantum phase transition or a breakdown of the weak-coupling RG approach. We show that the latter is more likely by adapting Dyson's argument for the breakdown of perturbative QED to the case of graphene. We propose future experiments and theoretical directions to make further progress on this important and difficult problem.

Abstract:
The Landau-Fermi liquid picture for quasiparticles assumes that charge carriers are dressed by many-body interactions, forming one of the fundamental theories of solids. Whether this picture still holds for a semimetal like graphene at the neutrality point, i.e., when the chemical potential coincides with the Dirac point energy, is one of the long-standing puzzles in this field. Here we present such a study in quasi-freestanding graphene by using high-resolution angle-resolved photoemission spectroscopy. We see the electron-electron and electron-phonon interactions go through substantial changes when the semimetallic regime is approached, including renormalizations due to strong electron-electron interactions with similarities to marginal Fermi liquid behavior. These findings set a new benchmark in our understanding of many-body physics in graphene and a variety of novel materials with Dirac fermions.

Abstract:
Theoretical studies have shown that electron-electron (e-e) and electron-hole (e-h) interactions play important roles in many observed quantum properties of graphene making this an ideal system to study many body effects. In this report we show that spectroscopic ellipsometry can enable us to measure this interactions quantitatively. We present spectroscopic data in two extreme systems of graphene on quartz (GOQ), an insulator, and graphene on copper (GOC), a metal which show that for GOQ, both e-e and e-h interactions dominate while for GOC e-h interactions are screened. The data further enables the estimation of the strength of the many body interaction through the effective fine structure constant, $\alpha_{g}^{*}$. The $\alpha_{g}^{*}$ for GOQ indicates a strong correlation with an almost energy independent value of about 1.37. In contrast, $\alpha_{g}^{*}$ value of GOC is photon energy dependent, is almost two orders of magnitude lower at low energies indicating very weak correlation.

Abstract:
We present an {\it ab initio} many-body GW calculation of the self-energy, the quasiparticle band plot and the spectral functions in free-standing undoped graphene. With respect to other approaches, we numerically take into account the full ionic and electronic structure of real graphene and we introduce electron-electron interaction and correlation effects from first principles. Both non-hermitian and also dynamical components of the self-energy are fully taken into account. With respect to DFT-LDA, the Fermi velocity is substantially renormalized and raised by a 17%, in better agreement with magnetotransport experiments. Furthermore, close to the Dirac point the linear dispersion is modified by the presence of a kink, as observed in ARPES experiments. Our calculations show that the kink is due to low-energy $\pi \to \pi^*$ single-particle excitations and to the $\pi$ plasmon. Finally, the GW self-energy does not open the band gap.

Abstract:
The optical properties of graphene are strongly affected by electron-electron (e-e) and electron-hole (e-h) interactions. Here we tune these many-body interactions through varying the density of free charge carriers. Measurements from the infrared to the ultraviolet reveal significant changes in the optical conductivity of graphene for both electron and hole doping. The shift, broadening, and modification in shape of the saddle-point exciton resonance reflect strong screening of the many-body interactions by the carriers, as well as changes in quasi-particle lifetimes. Ab initio calculations by the GW Bethe-Salpeter equation (GW-BSE), which take into account modification of both the repulsive e-e and the attractive e-h interactions, provide excellent agreement with experiment. Understanding the optical properties and high-energy carrier dynamics of graphene over a wide range of doping is crucial for both fundamental graphene physics and for emerging applications of graphene in photonics.