Theory of 2D transport in graphene for correlated disorder

We theoretically revisit graphene transport properties as a function of carrier density, taking into account possible correlations in the spatial distribution of the Coulomb impurity disorder in the environment. We find that the charged impurity correlations give rise to a density-dependent graphene conductivity, which agrees well qualitatively with the existing experimental data. We also find, quite unexpectedly, that the conductivity could increase with increasing impurity density if there is sufficient interimpurity correlation present in the system. In particular, the linearity (sublinearity) of graphene conductivity at lower (higher) gate voltage is naturally explained as arising solely from impurity correlation effects in the Coulomb disorder.     

The metal insulator transition in two-dimensional systems with charged impurities

The motion of interacting electrons in an array of charged impurities in two dimensions is discussed within a generalized selfconsistent current relaxation theory. The ratio of impurity density n_i to electron density n_c, where the metal insulator transition takes place, is shown to depend on n_c and varies between 0.2 and 10. A comparison of the theory with mobility measurements of Na⁺ drift experiments in inversion layers is made.     

Electronic thermal conductivity in suspended and supported bilayer graphene

Electronic thermal conductivity κ_e is investigated, using Boltzmann transport equation approach, in a suspended and supported bilayer graphene (BLG) as a function of temperature and electron concentration. The electron scattering due to screened charged impurity, short-range disorder and acoustic phonon via deformation potential are considered for both suspended and supported BLG. Additionally, scattering due to surface polar phonons, is considered in supported BLG. In suspended BLG, calculated κ_e is compared with the experimental data leaving the phonon thermal conductivity. It is emphasized that κ_e is important in samples with very high electron concentration and reduced phonon thermal conductivity. κ_e is found to be about two times smaller in supported BLG compared to that in suspended BLG. With the reduced extrinsic disorders, in principle, the intrinsic scattering by acoustic phonons can set a fundamental limit on possible intrinsic κ_e.     

Low-field carrier transport properties in biased bilayer graphene

Based on a semiclassical Boltzmann transport equation in random phase approximation, we develop a theoretical model to understand low-field carrier transport in biased bilayer graphene, which takes into account the charged impurity scattering, acoustic phonon scattering, and surface polar phonon scattering as three main scattering mechanisms. The surface polar optical phonon scattering of carriers in supported bilayer graphene is thoroughly studied using the Rode iteration method. By considering the metal–BLG contact resistance as the only one free fitting parameter, we find that the carrier density dependence of the calculated total conductivity agrees well with that observed in experiment under different temperatures. The conductivity results also suggest that in high carrier density range, the metal–BLG contact resistance can be a significant factor in determining the BLG conductivity at low temperature, and both acoustic phonon scattering and surface polar phonon scattering play important roles at higher temperature, especially for BLG samples with a low doping concentration, which can compete with charged impurity scattering.     

Band topology and the quantum spin Hall effect in bilayer graphene

We consider bilayer graphene in the presence of spin-orbit coupling, in order to assess its behavior as a topological insulator. The first Chern number n for the energy bands of single-layer graphene and that for the energy bands of bilayer graphene are computed and compared. It is shown that for a given valley and spin, n for a Bernal-stacked bilayer is doubled with respect to that for the monolayer. This implies that this form of bilayer graphene will have twice as many edge states as single-layer graphene, which we confirm with numerical calculations and analytically in the case of an armchair terminated surface. Bernal-stacked bilayer graphene is a weak topological insulator, whose surface spectrum is susceptible to gap opening under spin-mixing perturbations. We assess the stability of the associated topological bulk state of bilayer graphene under various perturbations. In contrast, we show that AA-stacked bilayer graphene is not a topological insulator unless the spin-orbit coupling is bigger than the interlayer hopping. Finally, we consider an intermediate situation in which only one of the two layers has spin-orbit coupling, and find that although individual valleys have non-trivial Chern numbers for the case of Bernal stacking, the spectrum as a whole is not gapped, so the system is not a topological insulator.     

Ground state of graphene in the presence of random charged impurities

We calculate the carrier-density-dependent ground-state properties of graphene in the presence of random charged impurities in the substrate taking into account disorder and interaction effects nonperturbatively on an equal footing in a self-consistent theoretical formalism. We provide detailed quantitative results on the dependence of the disorder-induced spatially inhomogeneous two-dimensional carrier density distribution on the external gate bias, the impurity density, and the impurity location. We find that the interplay between disorder and interaction is strong, particularly at lower impurity densities. We show that, for the currently available typical graphene samples, inhomogeneity dominates graphene physics at low (< or approximately 10(12) cm(-2)) carrier density with the density fluctuations becoming larger than the average density.     

Transport properties of the disordered charged bose condensate in two dimensions

Analytical results for the frequency-dependent conductivity of a disordered two-dimensional interacting Bose condensate are presented. Charged and uncharged impurities are considered. We find that for weak disorder the condensate is a superfluid while for strong disorder it is an insulator (a Bose glass). At the superfluid-insulator transition point (at the critical boson densityN _c) the condensate exhibits metallic tranport properties. An loffe-Regel criterion for the transition point is derived. The conductivity at the transition point is of ordere ²/h (h is Planck's constant) and depends on the kind of disorder. For charged impurities (with impurity densityN _i) the conductivity (for a condensate of particles with charge 2e and forN _i=2N _c) at the transition point is given by _c =0.26x(2e)²/h. We discuss recent experiments on superconducting ultra-thin films and on high-T _c superconductors.     

Abnormal electronic transport in disordered graphene nanoribbon

We investigate the conductivity σ of graphene nanoribbons with zigzag edges as a function of Fermi energy E_F in the presence of the impurities with different potential range. The dependence of σ(E_F) displays four different types of behavior, classified to different regimes of length scales decided by the impurity potential range and its density. Particularly, low density of long range impurities results in an extremely low conductance compared to the ballistic value, a linear dependence of σ(E_F) and a wide dip near the Dirac point, due to the special properties of long range potential and edge states. These behaviors agree well with the results from a recent experiment by Miao et al. [Science 317 (2007) 1530 (SOM)].     

Crossed diagram contribution to the electron self-energy due to impurity scattering in a magnetic field

We consider the contribution of crossed diagrams to the self-energy for a system of free electrons and fixed point impurities in the presence of a strong magnetic field. At the peaks of the Shubnikov-de Haas (S.d.H.) oscillations the dependence on the impurity concentration of the crossed diagram is the same as in the generalized Born approximation (n _i ^2/3 ). Nevertheless, for the S.d.H. regime the contribution of the crossed diagrams is shown to be unimportant.     

Theory of charged impurity scattering in two-dimensional graphene

We review the physics of charged impurities in the vicinity of graphene. The long-range nature of Coulomb impurities affects both the nature of the ground state density profile and graphene’s transport properties. We discuss the screening of a single Coulomb impurity and the ensemble averaged density profile of graphene in the presence of many randomly distributed impurities. Finally, we discuss graphene’s transport properties due to scattering off charged impurities both at low and high carrier density.     

电子-杂质和电子-声子相互作用对石墨烯磁光导的影响

在外加垂直磁场的石墨烯系统中,基于格林函数方法以自能的形式理论研究了电荷杂质散射和光学声子散射中心对朗道能谱的影响,采用久保(Kubo)公式研究了单层石墨烯的磁光电导谱以及跃迁选择定则。具体计算中电子-杂质库仑相互作用考虑了介电环境的屏蔽效应,对由散射引起的自能以及单粒子格林函数做自洽计算,另外在强磁场下单杂质散射是一个很好的近似模型。理论计算结果表明电荷杂质散射引起朗道能级对称展宽;同时考虑电荷杂质和光学声子两类散射后态密度表现为非对称的展宽。研究结果表明磁光电导谱的峰值和强度强烈依赖于填充因子和态密度。     

On the dynamic conductivity for an electron-impurity system

The correlation function formula for the dynamic conductivity of a system of non-interacting electrons in the field of impurities is analyzed in terms of proper connected diagrams. By selecting those diagrams appropriate in the region of weak coupling and low impurity concentration, a set of coupled equations for the energy broadening γ (ω, ε, n_s) and the energy shift Δ(ω, ε, n_s) is derived, where both γ and Δ depend on the frequency ω of a probing field, the energy ε of the electron, and the concentration, n_g, of impurities. With the assumption of a finite range potential, these equations are solved. It is found that γ (ω, n_s) is smaller than that extrapolated value which the conventional expression γ₀ for the low-concentration collision frequency would predict, in the entire region studied, that the difference γ₀-γ becomes appreciable when the ratio of the average time between scatterings, τ_c, to the average duration of a scattering, τ_d, is 100 or less, that γ (ω, n_s) decreases monotonically from its static value γ (0, n_s), and becomes vanishingly small in the region ω≈1/τ_d, and that in the static limit (ω=0), γ=γ₀[1?(2/π) (γ₀τ_d)+…], that the energy shift Δ is positive, and increases from 0 and reach a peak of magnitude γ₀ as ω is raised from 0. By using the γ and Δ obtained, the dynamic conductivity σ(ω, n_s) for degenerated electrons is calculated. The deviation, σ-σ₀, from the conventional expression σ₀=(?i) (n_ee²/M) [ω-iΓ₀]^?1, (n_e]=number density of electrons), for 0°K, is appreciable when the ratio τ_c/τ_d is 100 or less. The field-term correction, which arises from the modification of the scattering due to the probing field, is found to be negligible in the entire region studied.     

Layer stacking dependence on thermoelectric properties of massive Dirac fermions in bilayer graphene

We numerically study the thermoelectric transport in AB- and AA-stacked bilayer graphene in the presence of a strong magnetic field and disorder. In the AB-stacked case, we find that the thermoelectric conductivities display different asymptotic behaviors, depending on the ratio between the temperature and the width of the disorder-broadened Landau levels (LLs), similar to those of monolayer graphene. In the high temperature regime, the transverse thermoelectric conductivity α _xy saturates to a universal value 5.54k _B e/h at the center of each LL, and displays a linear temperature dependence at low temperatures. The calculated Nernst signal has a peak with a height of the order of k _B /e, and the thermopower changes sign at the central LL. We attribute this unique behavior to the coexistence of particle and hole LLs. In the AA-stacked bilayer case, it is found that the thermoelectric transport properties are consistent with the behavior of a band insulator. The obtained results demonstrate the sensitivity of the thermoelectric conductivity to the band gap near the Dirac point.     

Influence of interlayer coupling and intra-layer Coulomb interaction on electronic transport in bilayer graphene

Calculations of renormalized perpendicular conductivity within Kubo formula employing single particle temperature dependent Green's function formalism for bilayer graphene has been attempted. On the basis of numerical analysis, perpendicular conductivity as a function of temperature, interlayer coupling, onsite Coulomb interaction and carrier concentration per site has been analyzed for both AA- and AB-stacked bilayer graphene. It is found that perpendicular conductivity increases with interlayer coupling and also with temperature at low temperatures while at higher temperatures, there is saturation in perpendicular conductivity. Influences of onsite Coulomb interaction and carrier concentration per site on perpendicular conductivity is just opposite to each other while onsite Coulomb energy suppresses the rate of increase of σ_⊥/σ_⊥0 with temperature, on the other hand increase in carrier density per site enhance this rate significantly. Finally, theoretically obtained results on temperature dependent perpendicular conductivity are viewed in terms of electronic transport data as well as recent theoretical works available in bilayer graphene.     

Magnetic impurities in a two-dimensional superfluid Fermi gas with spin-orbit coupling

We study magnetic impurities in a two dimensional superfluid Fermi gas with thespin-orbit coupling and find that the spin-orbit coupling makes some dramatic impacts onthe effects of magnetic impurities. For the single impurity problem, we find that thenumber of bound states localized around the magnetic impurity is doubled. For the finiteconcentration n of impurities, we find that the energy gap is reduced andthe density of states in the gapless region is greatly modified; there exists a gaplesssuperfluid and N(ω) ∝ ω in the smallω limit.     

Correlated charged impurity scattering in graphene

We study electron transport properties of graphene in the presence of correlated charged impurities via adsorption and thermal annealing of potassium atoms. For the same density of charged scattering centers, the sample mobility sensitively depends on temperature which sets the correlation length between the scatterers. The data are well-understood by a recent theory that allows us to quantitatively extract the temperature dependence of the correlation length. Impurity correlations also offer a self-consistent explanation to the puzzling sublinear carrier-density dependence of conductivity commonly observed in monolayer graphene samples on substrates.     

Tuning the effective fine structure constant in graphene: opposing effects of dielectric screening on short- and long-range potential scattering

We reduce the dimensionless interaction strength alpha in graphene by adding a water overlayer in ultrahigh vacuum, thereby increasing dielectric screening. The mobility limited by long-range impurity scattering is increased over 30%, due to the background dielectric constant enhancement leading to a reduced interaction of electrons with charged impurities. However, the carrier-density-independent conductivity due to short-range impurities is decreased by almost 40%, due to reduced screening of the impurity potential by conduction electrons. The minimum conductivity is nearly unchanged, due to canceling contributions from the electron-hole puddle density and long-range impurity mobility. Experimental data are compared with theoretical predictions with excellent agreement.     

Nonmagnetic impurity effects and neutron scattering spectrum in iron pnictides

We study the effect of local impurity and the neutron scattering spectrum based on the five-orbital model obtained by the first principle calculation for iron pnictides. We find that the interband impurity scattering is induced by the complex multiorbital structure. This fact means that the fully-gapped sign-reversing s-wave state, which is predicted by spin-fluctuation theories, is very fragile against impurities. The result suggests a reasonable possibility that the fully-gapped s-wave state without sign reversal (s₊₊-wave) would be realized in dirty iron pnictides. We also find that broad peak structure observed in the neutron scattering measurements can be explained by the s₊₊-wave state.     

Impact of calcium on transport property of graphene

We have measured the impact of calcium adsorbates on the transport property of graphene. Although calcium renders conductivity linearly dependent on the carrier density of graphene as predicted, our experimental results diverge from the existing theoretical calculations. Our data expose the inadequacy of any existing theory to describe the minimum conductivity of graphene and indicate that a more complete testing of the impurity scattering calculations will require improving the experimental capabilities by minimizing the contribution from the substrate-bound charged impurities and developing an ability to count the number of adsorbates while measuring transport.