We review the problem of electron-electron interactions in graphene. Starting from screening long range these systems, we discuss existence an emerging Dirac liquid Lorentz invariant quasi-particles weak coupling regime, and strongly correlated electronic states strong regime. also analyze analogy connections between many-body Coulomb impurity problem. The magnetic instability Kondo effect impurities and/or adatoms graphene is discussed with classical models effects ordinary metals. show...

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

We propose a family of free fermion lattice models that have "Dirac loops", closed lines Dirac nodes in momentum space, on which the density states vanishes linearly with energy. Those lattices all possess planar trigonal connectivity present graphene, but are three dimensional. show their highly anisotropic and multiply-connected Fermi surface leads to quantized Hall conductivities dimensions for magnetic fields toroidal geometry. In presence spin-orbit coupling, we those structures...

We address the effective tight-binding Hamiltonian that describes insulating Mott state of twisted graphene bilayers at a magic angle. In configuration, form honeycomb superlattice localized states, characterized by appearance flat bands with four-fold degeneracy. After calculating maximally Wannier wavefunctions, we derive spin model state. suggest system is an exotic ferromagnetic insulator, well defined experimental signatures.

We examine the conditions necessary for presence of localized magnetic moments on adatoms with inner shell electrons in graphene. show that low density states at Dirac point, and anomalous broadening adatom electronic level, lead to formation arbitrarily small local charging energy. As a result, we obtain an scaling boundary separating nonmagnetic states. that, unlike any other material, can be controlled by electric field effect.

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 spectral gap in despite lattice mismatch. The origin is particularly intuitive regime strong coupling between and its substrate, when low-energy physics determined by topology network zero-energy modes. For twisted bilayers, where inversion symmetry present, percolates through system spectrum gapless. breaking causes modes to close into...

We examine the exchange Hamiltonian for magnetic adatoms in graphene with localized inner shell states. On symmetry grounds, we predict existence of a class orbitals that lead to distinct quantum critical points graphene, where Kondo temperature scales as ${T}_{K}\ensuremath{\propto}|J\ensuremath{-}{J}_{c}{|}^{1/3}$ near coupling ${J}_{c}$, and local spin is effectively screened by super-Ohmic bath. For this class, RKKY interaction decays spatially fast power law...

Electrons in graphene behave like Dirac fermions, permitting phenomena from high energy physics to be studied 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 image the dynamical screening charge freestanding, sheet. found that polarizability fermions amplified excitonic effects, improving interactions...

A central mystery in high temperature superconductivity is the origin of so-called "strange metal," i.e., anomalous conductor from which emerges at low temperature. Measuring dynamic charge response copper-oxides, $\chi''(q,\omega)$, would directly reveal collective properties strange metal, but it has never been possible to measure this quantity with meV resolution. Here, we present first measurement $\chi''(q,\omega)$ for a cuprate, optimally doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ ($T_c=91$...

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

We examine theoretically the signatures of magnetic adatoms in graphene probed by scanning tunneling spectroscopy (STS). When adatom hybridizes equally with two sublattices, broadening local level is anomalous and can scale cube energy. In contrast to ordinary metal surfaces, moment be suppressed proximity probing tip. propose that dependence conductance on distance between tip provide a clear signature for presence moments. also show distinguish whether located top carbon atom or center...

In contrast to conventional metals, so-called strange metals lack well-defined plasmons, exhibiting instead a featureless continuum that is key test of theories aimed at describing this phase matter.

The characteristic excitation of a metal is its plasmon, which quantized collective oscillation electron density. In 1956, David Pines predicted that distinct type dubbed 'demon', could exist in three-dimensional (3D) metals containing more than one species charge carrier1. Consisting out-of-phase movement electrons different bands, demons are acoustic, electrically neutral and do not couple to light, so have never been detected an equilibrium, 3D metal. Nevertheless, believed be critical...

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

We describe the formation of superconducting states in graphene presence pseudo-Landau-levels induced by strain, when time reversal symmetry is preserved. show that superconductivity strained quantum critical are completely filled, whereas at partial fillings survives weak coupling. In coupling limit, temperature scales linearly with strength and shows a sequence points as function filling factor can be accessed experimentally. argue electron-phonon transition controlled amount strain...

Excitons are the neutral quasiparticles that form when Coulomb interactions create bound states between electrons and holes. Due to their bosonic nature, excitons expected condense exhibit superfluidity at sufficiently low temperatures. In interacting Chern insulators, may inherit nontrivial topology quantum geometry from underlying electron wavefunctions. We theoretically investigate excitonic in flat-band insulators pumped with light. find exciton wavefunctions vortex structures momentum...

Although quasiparticles in flat bands have zero group velocity, they can display an anomalous velocity due to the quantum geometry. We address thermal and thermoelectric transport clean limit with a small amount of broadening inelastic scattering. derive general Kubo formulas for DC up linear order extract expressions conductivity, Seebeck Nernst coefficients. show that coefficient Chern is topological second corrections broadening. identify signatures two generic also generalized flattened...

We discuss the effect of electron-electron interactions on static polarization properties graphene beyond RPA. Divergent self-energy corrections are naturally absorbed into renormalized coupling constant $\ensuremath{\alpha}$. find that lowest-order vertex correction, which is first nontrivial correlation contribution, finite, and about 30% RPA result at strong $\ensuremath{\alpha}\ensuremath{\sim}1$. The correction leads to further reduction effective charge. Finite contributions dielectric...

We explore the physical properties of a unified microscopic theory for coexistence superconductivity and charge-density waves (CDWs) in two-dimensional transition-metal dichalcogenides. In case particle-hole symmetry, elementary particles are Dirac fermions at nodes charge density wave gap. When symmetry is broken, electron (hole) pockets formed around Fermi surface. The superconducting ground state emerges from pairing nodal quasiparticles mediated by acoustic phonons via piezoelectric...

We perform Monte Carlo simulations to study the interplay of structural and magnetic order in single layer graphene covered with adatoms. propose that presence ripples structure can lead clustering adatoms a variety states such as superparamagnetism, antiferromagnetism, ferromagnetism spin-glass behavior. derive magnetization hysteresis also magnetoresistance curves variable range hopping regime, which provide experimental signatures for ripple induced magnetism. be controlled by gate...

Vertical graphene heterostructures made up of layers separated by boron nitride spacers allow for novel ways tuning the interactions between electrons. We study possibility electron pairing mediated modified repulsive interactions. Long-range intravalley and short-range intervalley give rise to different anisotropic phases. show that a superconducting state with gaps opposite signs in valleys, an odd momentum state, can exist above carrier densities...

Two-dimensional semi-Dirac fermions are quasiparticles that disperse linearly in one direction and quadratically the other. We investigate instabilities of toward charge spin density wave superconducting orders, driven by short-range interactions. analyze critical behavior Yukawa theories for different order parameters using Wilson momentum shell renormalization group. generalize to a large number ${N}_{f}$ fermion flavors achieve analytic control $2+1$ dimensions calculate exponents at...