Jason Horng, Chi-Fan Chen, Baisong Geng, Caglar Girit, Yuanbo Zhang, Zhao Hao, Hans A. Bechtel, Michael Martin, Alex Zettl, Michael F. Crommie, Y. Ron Shen, Feng Wang
Electrons moving in graphene behave as massless Dirac fermions, and they exhibit fascinating low-frequency electrical transport phenomena. Their dynamic response, however, is little known at frequencies above one terahertz (THz). Such knowledge is important not only for a deeper understanding of the Dirac electron quantum transport, but also for graphene applications in ultrahigh speed THz electronics and IR optoelectronics. In this paper, we report the first measurement of high-frequency conductivity of graphene from THz to mid-IR at different carrier concentrations. The conductivity exhibits Drude-like frequency dependence and increases dramatically at THz frequencies, but its absolute strength is substantially lower than theoretical predictions. This anomalous reduction of free electron oscillator strength is corroborated by corresponding changes in graphene interband transitions, as required by the sum rule. Our surprising observation indicates that many-body effects and Dirac fermion-impurity interactions beyond current transport theories are important for Dirac fermion electrical response in graphene.
We study the dependence on the strength and orientation of applied uniaxial strain of the Drude weight in the conductivity of graphene. We find a nonmonotonic dependence on strain, which may be related to the proximity to several strain-induced electronic topological transitions. Given the relation between the Drude weight and the long-wavelength plasmon frequency, such a strain dependence can be evidenced by infrared spectroscopy measurements.
We theoretically reveal a new mechanism of light amplification in graphene under the conditions of interband population inversion. It is enabled by the indirect interband transitions, with the photon emission preceded or followed by the scattering on disorder. The emerging contribution to the optical conductivity, which we call the interband Drude conductivity, appears to be negative for the photon energies below the double quasi-Fermi energy of pumped electrons and holes. We find that for the Gaussian correlated distribution of scattering centers, the real part of the net Drude conductivity (…
The recent experimental study of the far-infrared transmission spectroscopy of monolayer graphene has shown that the Drude peak width increases by more than $10\%$ per $1\%$ of applied mechanical strain, while the Drude weight remains unchanged. We study the influence of the strain on the resonant impurity scattering. We propose a mechanism of augmentation of the scattering rate due to the shift in the position of resonance. Using the Lifshitz model of substitutional impurities, we investigate changes in the Drude peak weight and width as functions of the Fermi energy, impurity concentration a…
We present a theory of the influence of band renormalization and excitonic electron-electron interaction effects on the optical conductivity $σ(ω)$ of doped bilayer graphene. Using the Keldysh formalism, we derive a kinetic equation from which we extract numerical and approximate analytic results for $σ(ω)$. Our calculations reveal a previously unrecognized mechanism which couples the Drude and interband response and renormalizes the plasmon frequency, and suggest that screening must play an essential role in explaining the weakly renormalized conductivity seen in recent experiments.
We investigated the transient photoconductivity of graphene at various gate-tuned carrier densities by optical-pump terahertz-probe spectroscopy. We demonstrated that graphene exhibits semiconducting positive photoconductivity near zero carrier density, which crosses over to metallic negative photoconductivity at high carrier density. Our observations are accounted for by considering the interplay between photo-induced changes of both the Drude weight and the carrier scattering rate. Notably, we observed multiple sign changes in the temporal photoconductivity dynamics at low carrier density. T…
We develop a theory for the optical conductivity of doped multilayer graphene including the effects of electron-electron interactions. Applying the quantum kinetic formalism, we formulate a set of pseudospin Bloch equations that governs the dynamics of the nonequilibrium density matrix driven by an external \emph{a.c.} electric field under the influence of Coulomb interactions. These equations reveal a dynamical mechanism that couples the Drude and interband responses arising from the chirality of pseudospin textures in multilayer graphene systems. We demonstrate that this results in an intera…
We present detailed theoretical study on zero-frequency Drude weight and optical conductivity of a two-dimensional heavy-hole gas(2DHG) with $k$-cubic Rashba and Dresselhaus spin-orbit interactions. The presence of $k$-cubic spin-orbit couplings strongly modifies the Drude weight in comparison to the electron gas with $k$-linear spin-orbit couplings. For large hole density and strong $k$-cubic spin-orbit couplings, the density dependence of Drude weight deviates from the linear behavior. We establish a relation between optical conductivity and the Berry connection. Unlike two-dimensional elect…
We numerically calculate the optical conductivity of twisted graphene bilayers within the continuum model. To obtain the imaginary part, we employ the regularized Kramers-Kronig relation allowing us to discuss arbitrary twist angles, chemical potential and temperature. We find that the Drude weight $D$ as function of the chemical potential $μ$ closely follows the shell structure of twisted bilayer displayed by the density of states. For certain angles, this results in a transport gap D=0 at finite $μ$. We also discuss the loss function which, for low doping, is characterized by acoustic interb…
We demonstrate that the plasmon frequency and Drude weight of the electron liquid in a doped graphene sheet are strongly renormalized by electron-electron interactions even in the long-wavelength limit. This effect is not captured by the Random Phase Approximation (RPA), commonly used to describe electron fluids and is due to coupling between the center of mass motion and the pseudospin degree of freedom of the graphene's massless Dirac fermions. Making use of diagrammatic perturbation theory to first order in the electron-electron interaction, we show that this coupling enhances both the plas…
Graphene is a mechanically robust 2D material promising for flexible optoelectronic applications. However, its electromagnetic properties under strain are experimentally poorly understood. Here we present the far-infrared transmission spectra of large-area chemical-vapor deposited monolayer graphene on a polyethylene terephthalate substrate subjected to uniaxial strain. The effective strain value is calibrated using the Raman spectroscopy and corrected for a relaxation of wrinkles and folds seen directly by atomic-force microscopy. We find that while the Drude weight and the Fermi level remain…
Graphene, a monolayer of carbon atoms arranged in a hexagonal pattern, provides a unique two-dimensional (2D) system exhibiting exotic phenomena such as quantum Hall effects, massless Dirac quasiparticle excitations and universal absorption & conductivity. The linear energy-momentum dispersion relation in graphene also offers the opportunity to mimic the physics of far-away relativistic particles like neutron stars and white dwarfs. In this letter, we perform a counterintuitive ultrafast pump-probe experiment with high photon energies to isolate the Drude-like intraband dynamics of photoexcite…
Using Terahertz Time-Domain Spectroscopy, we study the temperature-dependent complex optical conductivity of the topological insulator, Bi$_{1.5}$Sb$_{0.5}$Te$_{1.8}$Se$_{1.2}$ single-crystal from 5 K to 150 K in the terahertz regime (0.4 -- 3.0 THz). We analyze our experimental results using the Drude-Lorentz model, with the Drude component representing the metallic surface state and the Lorentz term representing the bulk insulating state. We find the conductivity to be dominated by the Drude contribution, suggesting the presence of metallic surface states. The low-frequency real conductivity…
We show that the conductivity of a two-dimensional electron gas can be intrinsically anisotropic despite isotropic Fermi surface, energy dispersion, and disorder configuration. In the model we study, the anisotropy stems from the interplay between Dirac and Schrödinger features combined in a special two-band Hamiltonian describing the quasiparticles similar to the low-energy excitations in phosphorene. As a result, even scalar isotropic disorder scattering alters the nature of the carriers and results in anisotropic transport. Solving the Boltzmann equation exactly for such carriers with point…
This letter presents a generalization of the Drude conductivity for systems which are exposed to periodic driving. The probe bias is treated perturbatively by using the Kubo formula, whereas the external driving is included non-perturbatively using the Floquet theory. Using a new type of four-times Green's functions disorder is approached diagrammatically, yielding a fully analytical expression for the Floquet-Drude conductivity. Furthermore, the Floquet Fermi's golden rule is generalized to $tt'$-Floquet states, connecting the Floquet-Dyson series with scattering theory for Floquet states. Ou…
An explanation is proposed for the recently observed in optical spectra of monolayer graphene giant increase in the Drude peak width under applied uniaxial strain. We argue that the underlying mechanism of this increase can be based on resonant scattering of carriers from inevitably present impurities such as adsorbed atoms that can be described by the Fano-Anderson model. We demonstrate that the often neglected scalar deformation potential plays the essential role in this process. The conditions necessary for the maximum effect of the giant Drude peak broadening are determined. It is stressed…
We study electrical and optical conductivities of hole gas in $p$-doped bulk III-V semiconductors described by the Luttinger Hamiltonian. We provide exact analytical expressions of the Drude conductivity, inverse relaxation time for various impurity potentials, Drude weight and optical conductivity in terms of the Luttinger parameters $γ_1 $ and $γ_2$. The back scattering is completely suppressed as a result of the helicity conservation of the heavy and light hole states. We find that the inverse relaxation time of heavy holes is much less than that of the light holes for Coulomb-type and Gaus…
We report on absolute magneto-transmission experiments on highly-doped quasi-free-standing epitaxial graphene targeting the classical-to-quantum crossover of the cyclotron resonance. This study allows us to directly extract the carrier density and also other relevant quantities such as the quasiparticle velocity and the Drude weight, which is precisely measured from the strength of the cyclotron resonance. We find that the Drude weight is renormalized with respect to its non-interacting (or random-phase-approximation) value and that the renormalization is tied to the quasiparticle velocity enh…
We present a numerical model study of the zero-temperature infrared optical properties of (III,Mn)V diluted magnetic semiconductors. Our calculations demonstrate the importance of treating disorder and interaction effects simultaneously in modelling these materials. We find that the conductivity has no clear Drude peak, that it has a broadened inter-band peak near 220 meV, and that oscillator weight is shifted to higher frequencies by stronger disorder. These results are in good qualitative agreement with recent thin film absorption measurements. We use our numerical findings to discuss the us…
We present a numerical study on the intraband optical conductivity of hot carriers at quasi-equilibria in photoexcited graphene based on the semiclassical Boltzmann transport equations (BTE) with the aim of understanding the effects of intrinsic optical phonon and extrinsic coulomb scattering caused by charged impurities at the graphene--substrate interface. Instead of using full-BTE solutions, we employ iterative solutions of the BTE and the comprehensive model for the temporal evolutions of hot-carrier temperature and hot-optical-phonon occupations to reduce computational costs. Undoped grap…
We present a detail theoretical study of the Drude weight and optical conductivity of 8-$Pmmn$ borophene having tilted anisotropic Dirac cones. We provide exact analytical expressions of $xx$ and $yy$ components of the Drude weight as well as maximum optical conductivity. We also obtain exact analytical expressions of the minimum energy ($ε_1$) required to trigger the optical transitions and energy ($ε_2$) needed to attain maximum optical conductivity. We find that the Drude weight and optical conductivity are highly anisotropic as a consequence of the anisotropic Dirac cone. The optical condu…
Plasmons in ordinary electron liquids are collective excitations whose long-wavelength limit is rigid center-of-mass motion with a dispersion relation that is, as a consequence of Galileian invariance, unrenormalized by many-body effects. The long-wavelength plasmon frequency is related by the f-sum rule to the integral of the conductivity over the electron-liquid's Drude peak, implying that transport properties also tend not to have important electron-electron interaction renormalizations. In this article we demonstrate that the plasmon frequency and Drude weight of the electron liquid in a d…
The Dicke model of cavity quantum electrodynamics is approximately realized in condensed matter when the cyclotron transition of a two-dimensional electron gas is nearly resonant with a cavity photon mode. We point out that in the strong coupling limit the Dicke model of cavity cyclotron resonance must be supplemented by a term that is quadratic in the cavity photon field and suppresses the model's transition to a super-radiant state. We develop the theory of graphene cavity cyclotron resonance and show that the quadratic term, which is absent in graphene's low-energy Dirac model Hamiltonian, …
Using the Kubo linear response formalism, we study the effects of intrinsic graphene optical and surface polar phonons (SPPs) on the optical conductivity of doped graphene. We find that inelastic electron-phonon scattering contributes significantly to the phonon-assisted absorption in the optical gap. At room temperature, this midgap absorption can be as large as 20-25% of the universal ac conductivity for graphene on polar substrates due to strong electron-SPP coupling. The midgap absorption, moreover, strongly depends on the substrates and doping levels used. With increasing temperature, the…
We consider transport of dilute two-dimensional electrons, with temperature between Fermi and Debye temperatures. In this regime, electrons form a nondegenerate plasma with mobility limited by potential disorder. Different kinds of impurities contribute unique signatures to the resulting temperature-dependent Drude conductivity, via energy-dependent scattering. This opens up a way to characterize sample disorder composition. In particular, neutral impurities cause a slow decrease in conductivity with temperature, whereas charged impurities result in conductivity growing as a square root of tem…
In this work the Casimir{Polder interaction energy between a rubidium atom and a disordered graphene sheet is investigated beyond the Dirac cone approximation by means of accurate real-space calculations. As a model of defected graphene, we consider a tight-binding model of Π-electrons on a honeycomb lattice with a small concentration of point defects. The optical response of the graphene sheet is evaluated with full spectral resolution by means of exact Chebyshev polynomial expansions of the Kubo formula in large lattices with in excess of ten million atoms. At low temperatures, the optical r…
The gapless energy band spectra make the structures based on graphene and graphene bilayers with the population inversion created by optical or injection pumping to be promising media for the interband terahertz (THz) lasing. However, a strong intraband absorption at THz frequencies still poses a challenge for efficient THz lasing. In this paper, we show that in the pumped graphene bilayer structures, the indirect interband radiative transitions accompanied by scattering of carriers caused by disorder can provide a substantial negative contribution to the THz conductivity (together with the di…
The thermal conductivity of graphene nanoribbons (layer from 1 to 8 atomic planes) is investigated by using the nonequilibrium molecular dynamics method. We present that the room-temperature thermal conductivity decays monotonically with the number of the layers in few-layer graphene. The superiority of zigzag graphene in thermal conductivity is only available in high temperature region and disappears in multi-layer case. It is explained that the phonon spectral shrink in high frequency induces the change of thermal conductivity. It is also reported that single-layer graphene has better ballis…
We consider the tight-binding approximation for the description of energy bands of graphene, together with the standard Boltzmann's transport equation and constant relaxation time, an expression for the conductivity was obtained. We predicted strong nonlinear effects in graphene which may be useful for high frequency generation.
The analysis of Current-voltage characteristic and Ampere-Gauss characteristic for graphene with Hubbard interaction was carried out depending on frequency of external variable field and magnetic field. The regions of the absolute negative conductivity were found.
Transport properties of irradiated graphene (electrical conductivity and mobility) are numerically investigated using the real-space Kubo formalism. A micrometer-sized system consisting of millions of atoms with nanopores of various sizes and concentrations is described. Electrical conductivity and mobility as a function of carrier (hole) density are calculated to provide possible comparisons with experiments.
Disordered Fermi-Dirac distributions are used to model, within a straightforward and essentially phenomenological Boltzmann equation approach, the electron/hole transport across graphene puddles. We establish, with striking experimental support, a functional relationship between the graphene minimum conductivity, the mobility in the Boltzmann regime, and the steepness of the conductivity parabolic profile usually observed through gate-voltage scanning around the charge neutral point.
Using the Landauer formula approach, it is proven that minimal conductivity of order of $e^{2}/h$ found experimentally in bilayer graphene is its intrinsic property. For the case of ideal crystals, the conductivity turns our to be equal to $e^{2}/2h$ per valley per spin. A zero-temperature shot noise in bilayer graphene is considered and the Fano factor is calculated. Its value $1-2/π$ is close to the value 1/3 found earlier for the single-layer graphene.
We study thermal transport in folded graphene nanoribbons using molecular dynamics simulations and the non-equilibrium Green's function method. It is found that the thermal conductivity of flat graphene nanoribbons can be modulated by folding and changing interlayer couplings. The analysis of transmission reveals that the reduction of thermal conductivity is due to scattering of low frequency phonons by the folds. Our results suggest that folding can be utilized in the modulation of thermal transport properties in graphene and other two dimensional materials.
Using non-equilibrium molecular dynamics method(NEMD), we have found that the thermal conductivity of multilayer graphene nanoribbons monotonously decreases with the increase of the number of layers, such behavior can be attributed to the phonon resonance effect of out-of-plane phonon modes. The reduction of thermal conductivity is found to be proportional to the layer size, which is caused by the increase of phonon resonance. Our results are in agreement with recent experiment on dimensional evolution of thermal conductivity in few layer graphene.
In this study, the Optical conductivity of substitutionary doped graphene is investigated in presence of the Rashba spin orbit coupling (RSOC). Calculations have been performed within the coherent potential approximation (CPA) beyond the Dirac cone approximation. Results of the current study demonstrate that the optical conductivity is increased by increasing the RSOC strength. Meanwhile it was observed that the anisotropy of the band energy results in a considerable anisotropic optical conductivity (AOC) in monolayer graphene. The sign and magnitude of this anisotropic conductivity was shown …
Second-order dc conductivity in the velocity-gauge Keldysh formalism: gauge-invariant decomposition into nonlinear Drude, Berry-curvature-dipole, and quantum-metric responses
We address the tunneling current in a graphene-hBN-graphene heterostructure as function of the twisting between the crystals. The twisting induces a modulation of the hopping amplitude between the graphene layers, that provides the extra momentum necessary to satisfy momentum and energy conservation and to activate coherent tunneling between the graphene electrodes. Conservation rules limit the tunneling to states with wavevectors lying at the conic curves defined by the intersection of two Dirac cones shifted in momentum and energy. There is a critical voltage where the intersection is a stra…
Conductivity of monolayer and two-layer graphene is considered with due regard for mutual drag of band electrons and holes. Search of contribution of the drag in conductivity shows that this effect can sufficiently influence on mobility of carriers, which belong to different groups and have different drift velocities. In two-layer system the mutual drag can even change the di-rection of partial current in separate layer.
Using the linearized Boltzmann transport equation and perturbation theory, we analyze the reduction in the intrinsic thermal conductivity of few-layer graphene sheets accounting for all possible three-phonon scattering events. Even with weak coupling between layers, a significant reduction in the thermal conductivity of the out-of-plane acoustic modes is apparent. The main effect of this weak coupling is to open many new three-phonon scattering channels that are otherwise absent in graphene. However, reflection symmetry is only weakly broken with the addition of multiple layers, and ZA phonons…
We theoretically study the population inversion and negative dynamic conductivity in intrinsic graphene in the terahertz (THz) frequency range upon pulse photoexcitation with near-/mid-infrared wavelength. The threshold pulse energy required for the population inversion and negative dynamic conductivity can be orders-of-magnitude lower when the pulse photon energy is lower, due to the inverse proportionality of the photoexcited carrier concentration to the pulse photon energy and to the weaker carrier heating. We also investigate the dependence of the dynamic conductivity on the momentum relax…
We develop the theory of heat conductivity in supported graphene, accounting for coherent phonon scattering on disorder induced by an amorphous substrate. We derive spectra for in-plane and out-of-plane phonons in the framework of Green's function approach. The energetic parameters of the theory are obtained using the molecular dynamics simulations for graphene on SiO$_2$ substrate. The heat conductivity is calculated by the Boltzmann transport equation. We find that the interaction with the substrate drastically reduces the phonon lifetime and completely suppresses the contribution of ZA phon…
In a heavily doped semiconductor with weak spin-orbital interaction the Dyakonov-Perel spin relaxation rate is known to be proportional to the Drude conductivity. We argue that in the case of weak spin-orbital interaction this proportionality goes beyond the Drude mechanism: it stays valid through the metal-insulator transition and in the range of the exponentially small hopping conductivity.
As a low-energy effective theory on non-symmorphic lattices, we consider a generic triple point fermion Hamiltonian which is parameterized by an angular parameter $λ$. We find strong $λ$ dependence in both Drude and interband optical absorption of these systems. The deviation of the $T^2$ coefficient of the Drude weight from Dirac/Weyl fermions can be used as a quick way to optically distinguish the triple point degeneracies from the Dirac/Weyl degeneracies. At the particular $λ=π/6$ point, we find that the "helicity" reversal optical transition matrix element is identically zero. But deviatin…
Using terahertz time-domain spectroscopy, the real part of optical conductivity [$σ_{1}(ω)$] of twisted bilayer graphene was obtained at different temperatures (10 -- 300 K) in the frequency range 0.3 -- 3 THz. On top of a Drude-like response, we see a strong peak in $σ_{1} (ω)$ at $\sim$2.7 THz. We analyze the overall Drude-like response using a disorder-dependent (unitary scattering) model, then attribute the peak at 2.7 THz to an enhanced density of states at that energy, that is caused by the presence of a van Hove singularity arising from a commensurate twisting of the two graphene layers…
The minimum conductivity value as well as the linear dependence of conductivity on the charge density near the Dirac point in single and doublelayer graphene is derived from the energy-time uncertainty principle applied to ballistic charge carriers.
In the recent paper [arXiv:0802.2216, 15 Feb 2008], Kashuba argued that the intrinsic conductivity of graphene independent of temperature originated in strong electron-hole scattering. We propose a much more explicit derivation based on a scaling theory approach. We also give an explanation of a rapid increase in graphene conductivity caused by applied gate voltage.
The thermal conductivity of doped graphene flake of finite size is investigated with emphasis on the influence of mass of substituting atoms on this property. It is shown that the graphene doping by small concentrations of relatively heavy atoms results in a disproportionately impressive drop of lattice thermal conductivity.
Graphene has a high intrinsic thermal conductivity and a high electron mobility. The thermal conductivity of graphene can be significantly reduced when different carbon isotopes are mixed, which can enhance the performance of thermoelectric devices. Here we compare the thermal conductivities of isotopic c12/c13 random mixes with isotope superlattices with periods ranging from 46 to 225 nm. Raman Opto-Thermal conductivity measurements of these superlattice structures show an approximately 50% reduction in thermal conductivity compared to pristine c12 graphene. This average reduction is similar …
An exact solution is obtained for the electromagnetic field due to an electric current in the presence of a surface conductivity model of graphene. The graphene is represented by an infinitesimally-thin, local and isotropic two-sided conductivity surface. The field is obtained in terms of dyadic Green's functions represented as Sommerfeld integrals. The solution of plane-wave reflection and transmission is presented, and surface wave propagation along graphene is studied via the poles of the Sommerfeld integrals. For isolated graphene characterized by complex surface conductivity, a proper tra…
We study the conductivity of a graphene strip taking into account electrostatically-induced charge accumulation on its edges. Using a local dependency of the conductivity on the carrier concentration we find that the electrostatic size effect in doped graphene strip of the width of 0.5 - 3 $% μ$m can result in a significant (about 40%) enhancement of the effective conductivity in comparison to the infinitely wide samples. This effect should be taken into account both in the device simulation as well as for verification of scattering mechanisms in graphene.
We theoretically study current dynamics of graphene nanoribbons subject to bias dc and ac driven fields. We showed that graphene nanoribbons exhibit negative high-harmonic differential conductivity. Negative differential conductivity appears when bias electric filed is in the neighborhood of applied ac filed amplitude. We also observe both even and odd high-harmonic negative differential conductivity at wave mixing of two commensurate frequencies. The even harmonics are more pronounced than the odd harmonics. A possible use of the present method for generating terahertz frequencies at even har…
We investigate the conductivity of doped graphene in the semiclassical Boltzmann limit, as well as the conductivity minimum within the self-consistent transport theory. Using the hard-disk model for a two-dimensional distribution of impurities gives rise to both strong increase in the slope of conductivity at low charge carrier densities in graphene and a strongly sub-linear behavior of the conductivity at high charge carrier densities when the correlation distance between the impurities is large. On the other hand, we find that a super-linear dependence of the conductivity on charge carrier d…
Applying a quasiclassical equation to carriers in graphene we found a way how to distinguish between samples with the domination of short and long range scatterers from the conductivity measurements. The model proposed explains recent transport experiments with chemically doped as well as suspended graphene.
The conductivity of doped graphene is considered taking into account scattering by short-range nonsymmetric defects, when the longitudinal and transverse components of conductivity tensor appear to be different. The calculations of the anisotropic conductivity tensor are based on the quasiclassical kinetic equation for the case of monopolar transport at low temperatures. The effective longitudinal conductivity and the transverse voltage, which are controlled by orientation of sample and by gate voltage (i.e. doping level), are presented.
Utilizing a complete Lorentz-covariant and local-gauge-invariant formulation, we discuss graphene response to arbitrary external electric field. The relation, which is called as Kramers-Kr(\ddot{o})nig relation in the paper, between imaginary part and real part of ac conductivity is given. We point out there exists an ambiguity in the conductivity computing, attributed to the wick behavior at ultraviolet vicinity. We argue that to study electrical response of graphene completely, non-perturbational contribution should be considered.
We have investigated thermal conductivity of graphene laminate films deposited on polyethylene terephthalate substrates. Two types of graphene laminate were studied - as deposited and compressed - in order to determine the physical parameters affecting the heat conduction the most. The measurements were performed using the optothermal Raman technique and a set of suspended samples with the graphene laminate thickness from 9 to 44 micrometers. The thermal conductivity of graphene laminate was found to be in the range from 40 W/mK to 90 W/mK at room temperature. It was found unexpectedly that th…
We use linear-response theory to evaluate the frequency-dependent conductivity of a system subject to a continuous quantum measurement of the current. Application of this formalism to graphene yields a consistent framework for discussing nonuniversal values of its minimal conductivity.
The next-nearest neighbor interaction (NNN) is included in a tight-binding calculation of the electronic spectrum and conductivity of doped graphene. As a result, we observe a wide variation of the conductivity behavior, since the Fermi energy and the resonance peak are not shifted by the same amount. Such effect can have a profound effect in the idea of explaining the minimal conductivity of graphene as a consequence of impurities or defects. Finally, we also estimate the mean free path and relaxation time due to resonant impurity scattering.
