Coulomb Interaction In Graphene Research Articles

Hierarchy of information scrambling, thermalization, and hydrodynamic flow in graphene

We determine the information scrambling rate $\lambda_{L}$ due to electron-electron Coulomb interaction in graphene. $\lambda_{L}$ characterizes the growth of chaos and has been argued to give information about the thermalization and hydrodynamic transport coefficients of a many-body system. We demonstrate that $\lambda_{L}$ behaves for strong coupling similar to transport and energy relaxation rates. A weak coupling analysis, however, reveals that scrambling is related to dephasing or single particle relaxation. Furthermore, $\lambda_{L}$ is found to be parametrically larger than the collision rate relevant for hydrodynamic processes, such as electrical conduction or viscous flow, and the rate of energy relaxation, relevant for thermalization. Thus, while scrambling is obviously necessary for thermalization and quantum transport, it does generically not set the time scale for these processes. In addition we derive a quantum kinetic theory for information scrambling that resembles the celebrated Boltzmann equation and offers a physically transparent insight into quantum chaos in many-body systems.

Microscopic tight-binding study of the interplay between on-site and inter-site Coulomb interactions in Graphene

It is realized that the Coulomb interaction plays a vital role in describing the magnetic properties of graphene-on-substrate. We attempt here to study the competition between on-site and inter-site repulsive Coulomb interactions, with impurities at both the sub-lattices in graphene-on-substrate .The Hamiltonian describes the electron hopping up to third-nearest-neighbors within tight-binding approximation. Due to substrate effect, A-sub lattice is raised by energy and B-sub lattice acquired energy , besides impurity effects at both the sub lattices. The model consists of on-site repulsive Coulomb interaction at two sublattices with same on-site Coulomb energy U and nearest-neighbor inter-site Coulomb interactions between A and B sub lattice with inter site Coulomb energy . The Coulomb interaction is considered within Hartree-Fock type mean-field approximation. The Hamiltonian is solved by Zubarev's Green's function technique and an expression for temperature dependent difference in electron occupancies between two sub-lattices is calculated and solved self-consistency. Finally the charge gap and hence modified substrate induced gap is computed numerically by varying different physical parameters of the system like on-site and inter-site Coulomb interactions and substrate induced gap, impurity concentration and electron occupancy. It is observed that inter-site Coulomb interaction is smaller than on-site Coulomb interaction and plays an important role in describing the properties of graphene.

Förster-Induced Energy Transfer in Functionalized Graphene.

Carbon nanostructures are ideal substrates for functionalization with molecules since they consist of a single atomic layer giving rise to an extraordinary sensitivity to changes in their surrounding. The functionalization opens a new research field of hybrid nanostructures with tailored properties. Here, we present a microscopic view on the substrate–molecule interaction in the exemplary hybrid material consisting of graphene functionalized with perylene molecules. First experiments on similar systems have been recently realized illustrating an extremely efficient transfer of excitation energy from adsorbed molecules to the carbon substrate, a process with a large application potential for high-efficiency photovoltaic devices and biomedical imaging and sensing. So far, there has been no microscopically founded explanation for the observed energy transfer. Based on first-principle calculations, we have explicitly investigated the different transfer mechanisms revealing the crucial importance of Förster coupling. Due to the efficient Coulomb interaction in graphene, we obtain strong Förster rates in the range of 1/fs. We investigate its dependence on the substrate–molecule distance R and describe the impact of the momentum transfer q for an efficient energy transfer. Furthermore, we find that the Dexter transfer mechanism is negligibly small due to the vanishing overlap between the involved strongly localized orbital functions. The gained insights are applicable to a variety of carbon-based hybrid nanostructures.

The Lifshitz–Kosevich theory and Coulomb interaction in graphene

The influence of Coulomb interactions on the magnetic susceptibility, chemical potential and heat capacity in graphene is considered.

The electron many-body problem in graphene

We give a brief summary of the current status of the electron many-body problem in graphene. We claim that graphene has intrinsic dielectric properties which should dress the interactions among the quasiparticles, and may explain why the observation of electron–electron renormalization effects has been so elusive in the recent experiments. We argue that the strength of Coulomb interactions in graphene may be characterized by an effective fine structure constant given by α⋆(k, ω)≡2.2/ϵ(k, ω), where ϵ(k, ω) is the dynamical dielectric function. At long wavelengths, α⋆(k, ω) appears to have its smallest value in the static regime, where α⋆(k→0, 0)≈1/7 according to recent inelastic x-ray measurements, and the largest value in the optical limit, where α⋆(0, ω)≈2.6. We conclude that the strength of Coulomb interactions in graphene is not universal, but is highly dependent on the scale of the phenomenon of interest. We propose a prescription in order to reconcile different experiments.

Strength of Effective Coulomb Interactions in Graphene and Graphite

To obtain an effective many-body model of graphene and related materials from first principles we calculate the partially screened frequency dependent Coulomb interaction. In graphene, the effective on-site (Hubbard) interaction is U(00)=9.3 eV in close vicinity to the critical value separating conducting graphene from an insulating phase emphasizing the importance of nonlocal Coulomb terms. The nearest-neighbor Coulomb interaction strength is computed to U(01)=5.5 eV. In the long-wavelength limit, we find the effective background dielectric constant of graphite to be ϵ=2.5 in very good agreement with experiment.

Coulomb interaction in graphene: Relaxation rates and transport

We analyze the inelastic electron-electron scattering in undoped graphene within the Keldysh diagrammatic approach. We demonstrate that finite temperature strongly affects the screening properties of graphene, which, in turn, influences the inelastic-scattering rates as compared to the zero-temperature case. Focusing on the clean regime, we calculate the quantum scattering rate which is relevant for dephasing interference processes. We identify a hierarchy of regimes arising due to the interplay of a plasmon enhancement of the scattering and finite-temperature screening of the interaction. We further address the energy relaxation and transport scattering rates in graphene. We find a nonmonotonic energy dependence of the inelastic relaxation rates in clean graphene, which is attributed to the resonant excitation of plasmons. Finally, we discuss the temperature dependence of the conductivity at the Dirac point in the presence of both interaction and disorder. Our results complement the kinetic equation and hydrodynamic approaches for the collision-limited conductivity of clean graphene and can be generalized to the treatment of physics of inelastic processes in strongly nonequilibrium setups.

Competition between excitonic gap generation and disorder scattering in graphene

We study the disorder effect on the excitonic gap generation caused by strong Coulomb interaction in graphene. By solving the self-consistently coupled equations of dynamical fermion gap m and disorder scattering rate Γ, we have found a critical line on the plane of interaction strength λ and disorder strength g. The phase diagram is divided into two regions: in the region with large λ and small g, m≠0 and Γ=0; in the other region, m=0 and Γ≠0 for nonzero g. In particular, there is no coexistence of finite fermion gap and finite scattering rate. These results imply a strong competition between excitonic gap generation and disorder scattering. This conclusion does not change when an additional contact four-fermion interaction is included. For sufficiently large λ, the growing disorder may drive a quantum phase transition from an excitonic insulator to a metal.

Fractional quantum Hall effect in suspended graphene probed with two-terminal measurements

Recently, fractional quantization of two-terminal conductance was reported in suspended graphene. The quantization, which was clearly visible in fields as low as 2 T and persistent up to 20 K in 12 T, was attributed to the formation of an incompressible fractional quantum Hall state. Here, we argue that the failure of earlier experiments to detect the integer and fractional quantum Hall effect with a Hall-bar lead geometry is a consequence of the invasive character of voltage probes in mesoscopic samples, which are easily shorted out owing to the formation of hot spots near the edges of the sample. This conclusion is supported by a detailed comparison with a solvable transport model. We also consider, and rule out, an alternative interpretation of the quantization in terms of the formation of a p-n-p junction, which could result from contact doping or density inhomogeneity. Finally, we discuss the estimate of the quasi-particle gap of the quantum Hall state. The gap value, obtained from the transport data using a conformal mapping technique, is considerably larger than in GaAs-based two-dimensional electron systems, reflecting the stronger Coulomb interactions in graphene.

Renormalization of Coulomb interaction in graphene: Determining observable quantities

We address the computation of physical observables in graphene in the presence of Coulomb interactions of density-density type modeled with a static Coulomb potential within a quantum field theory perturbative renormalization scheme. We show that all the divergences encountered in the physical quantities are associated to the one loop electron self-energy and can be determined without ambiguities by a proper renormalization of the Fermi velocity. The renormalization of the photon polarization to second order in perturbation theory - a quantity directly related to the optical conductivity - is given as an example.

Supercritical Coulomb center and excitonic instability in graphene

It is well known that there are resonant states with complex energy for the supercritical Coulomb impurity in graphene. We show that opening of a quasiparticle gap decreases the imaginary part of energy, $|\text{Im}\text{ }E|$, of these states and stabilizes the system. For gapless quasiparticles with strong Coulomb interaction in graphene, we solve the Bethe-Salpeter equation for the electron-hole bound state and show that it has a tachyonic solution for strong enough coupling $\ensuremath{\alpha}={e}^{2}/\ensuremath{\kappa}\ensuremath{\hbar}{v}_{F}$ leading to instability of the system. In the random-phase approximation, the critical coupling is estimated to be ${\ensuremath{\alpha}}_{c}=1.62$ and is an analog of the critical charge in the Coulomb center problem. We argue that the excitonic instability should be resolved through the formation of an excitonic condensate and gap generation in the quasiparticle spectrum.

1/Nexpansion in correlated graphene

We examine the $1/N$ expansion, where $N$ is the number of two-component Dirac fermions for Coulomb interactions in graphene with a gap of magnitude $\ensuremath{\Delta}=2m$. We find that for $N\ensuremath{\alpha}⪢1$, where $\ensuremath{\alpha}$ is graphene's ``fine-structure constant,'' there is a crossover as a function of distance $r$ from the usual three-dimensional Coulomb law, $V(r)\ensuremath{\sim}1/r$, to a two-dimensional Coulomb interaction, $V(r)\ensuremath{\sim}\text{ln}(N\ensuremath{\alpha}/mr)$, for ${m}^{\ensuremath{-}1}⪡r⪡{m}^{\ensuremath{-}1}N\ensuremath{\alpha}/6$. This effect reflects the weak ``confinement'' of the electric field in the graphene plane. The crossover also leads to unusual renormalization of the quasiparticle velocity and gap at low momenta. We also discuss the differences between the interaction potential in gapped graphene and usual quantum electrodynamics for different coupling regimes.

Coulomb Interaction, Ripples, and the Minimal Conductivity of Graphene

We argue that the unscreened Coulomb interaction in graphene provides a positive, universal, and logarithmic correction to scaling of zero-temperature conductivity with frequency. The combined effect of the disorder due to wrinkling of the graphene sheet and the long-range electron-electron interactions is a finite positive contribution to the dc conductivity. This contribution is disorder strength dependent and thus nonuniversal. The low-energy behavior of such a system is governed by the line of fixed points at which both the interaction and disorder are finite, and the density of states is exactly linear. An estimate of the typical random vector potential representing ripples in graphene brings the theoretical value of the minimal conductivity into the vicinity of 4e2/h.