Conductivity of disordered graphene at half filling

We study electron transport properties of a monoatomic graphite layer (graphene) with different types of disorder at half filling. We show that the transport properties of the system depend strongly on the symmetry of disorder. We find that the localization is ineffective if the randomness preserves one of the chiral symmetries of the clean Hamiltonian or does not mix valleys. We obtain the exact value of minimal conductivity 4e²/πh in the case of chiral disorder. For long-range disorder (decoupled valleys), we derive the effective field theory. In the case of smooth random potential, it is a symplectic-class sigma-model including a topological term with θ=π. As a consequence, the system is at a quantum critical point with a universal value of the conductivity of the order of e²/h. When the effective time reversal symmetry is broken, the symmetry class becomes unitary, and the conductivity acquires the value characteristic for the quantum Hall transition.     

Quantum Hall effect of massless dirac fermions in a vanishing magnetic field

The effect of strong long-range disorder on the quantization of the Hall conductivity sigma{xy} in graphene is studied numerically. It is shown that increasing Landau-level mixing progressively destroys all plateaus in sigma{xy} except the plateaus at sigma{xy}=-/+e{2}/2h (per valley and per spin). The critical state at the Dirac point is robust to strong disorder and belongs to the universality class of the conventional plateau transitions in the integer quantum Hall effect. We propose that the breaking of time-reversal symmetry by ripples in graphene can realize this quantum critical point in a vanishing magnetic field.     

Quantum Hall effects in layered disordered superconductors

Layered singlet paired superconductors with disorder and broken time reversal symmetry are studied, demonstrating a phase diagram with charge-spin separation in transport. In terms of the average intergrain transmission and the interlayer tunneling we find quantum Hall phases with spin Hall coefficients of sigma(spin)(xy)=0,2 separated by a spin metal phase. We identify a spin metal-insulator localization exponent as well as a spin conductivity exponent of approximately 0.96. In the presence of a Zeeman term an additional sigma(spin)(xy)=1 phase appears.     

Effective potential of the O(N) linear sigma-model at finite temperature

We study the O(N) symmetric linear sigma-model at finite temperature as the low-energy effective models of quantum chromodynamics (QCD) using the Cornwall-Jackiw-Tomboulis (CJT) effective action for composite operators. It has so far been claimed that the Nambu-Goldstone theorem is not satisfied at finite temperature in this framework unless the large-N limit in the O(N) symmetry is taken. We show that this is not the case. The pion is always massless below the critical temperature, if one determines the propagator within the form such that the symmetry of the system is conserved, and defines the pion mass as the curvature of the effective potential. We use a regularization for the CJT effective potential in the Hartree approximation, which is analogous to the renormalization of auxiliary fields. A numerical study of the Schwinger-Dyson equation and the gap equation is carried out including the thermal and quantum loops. We point out a problem in the derivation of the sigma meson mass without quantum correction at finite temperature. A problem about the order of the phase transition in this approach is also discussed. Received: 21 June 2000 / Accepted: 13 September 2000     

High frequency conductivity in the quantum hall regime

We have measured the complex conductivity sigma(xx) of a two-dimensional electron system in the quantum Hall regime up to frequencies of 6 GHz at electron temperatures below 100 mK. Using both its imaginary and real part we show that sigma(xx) can be scaled to a single function for different frequencies and several transitions between plateaus in the quantum Hall effect. Additionally, the conductivity in the variable-range hopping regime is used for a direct evaluation of the localization length xi. Even for large filling factor distances deltanu from the critical point we find xi approximately equals deltanu(-gamma) with a scaling exponent gamma = 2.3.     

On the theory of galvanomagnetic properties of composites

The conductivity of composites in the presence of a magnetic field H is considered. The galvanomagnetic characteristics for a weakly inhomogeneous medium are determined in explicit form in an approximation quadratic in the deviations of conductivity tensor $\hat \sigma $ (r) from its mean value 〈 $\hat \sigma $ 〉. The contribution to the effective conductivity tensor $\hat \sigma _e $ linear in concentration c of inclusions for a composite with a small value of c is expressed in terms of the dipole polarizability of an individual inclusion, which is defined in the transformed system in which it is surrounded by an isotropic matrix with a scalar conductivity. Transition to this system is performed using a symmetry transformation that does not change the dc equations. An approximate approach proposed for describing the galvanomagnetic properties of composites in the wide range of parameters appearing in the problem generalizes the standard theory of an effective medium to the case of anisotropic systems with inclusions of arbitrary shape in field H ≠ 0.     

On the theory of conductivity of anisotropic composites: A weakly inhomogeneous medium

The conductivity of a weakly inhomogeneous anisotropic medium is considered. The effective conductivity tensor $ \hat \sigma _e $ \hat \sigma _e is determined in the approximation quadratic in deviation of local conductivity $ \hat \sigma $ \hat \sigma (r) from mean value 〈$ \hat \sigma $ \hat \sigma 〉 for an arbitrary anisotropy of the composite.     

Quantized anomalous Hall effect in two-dimensional ferromagnets: quantum Hall effect in metals

We study the effect of disorder on the anomalous Hall effect (AHE) in two-dimensional ferromagnets. The topological nature of the AHE leads to the integer quantum Hall effect from a metal, i.e., the quantization of sigma(xy) induced by the localization except for the few extended states carrying Chern numbers. Extensive numerical study on a model reveals that Pruisken's two-parameter scaling theory holds even when the system has no gap with the overlapping multibands and without the uniform magnetic field. Therefore, the condition for the quantized AHE is given only by the Hall conductivity sigma(xy) without the quantum correction, i.e., /sigma(xy)/>e(2)/(2h).     

Scaling of the magnetoconductivity of silicon MOSFETs: evidence for a quantum phase transition in two dimensions

For a broad range of electron densities n and temperatures T, the in-plane magnetoconductivity of the two-dimensional system of electrons in silicon MOSFETs can be scaled onto a universal curve with a single parameter H(sigma)(n,T), where H(sigma) obeys the empirical relation H(sigma) = A(n) [Delta(n)(2)+T2](1/2). The characteristic energy k(B)Delta associated with the magnetic field dependence of the conductivity decreases with decreasing density, and extrapolates to 0 at a critical density n(0), signaling the approach to a zero-temperature quantum phase transition. We show that H(sigma) = AT for densities near n(0).     

On the theory of conductivity of anisotropic composites: A linear-concentration approximation of inclusions

A general approach is proposed for calculating the conductivity of anisotropic composites with a low concentration of inclusions of an arbitrary shape. The contribution to effective conductivity [^(s)] _e\hat \sigma _e, which is linear in concentration, is expressed in terms of the polarizability of the inclusion defined in a certain transformed system in which the inclusion is surrounded by an isotropic matrix. A transition to this system is performed using a symmetry transformation that does not change the equations for direct current.     

Nonequilibrium quantum impurities: from entropy production to information theory

Nonequilibrium steady-state currents, unlike their equilibrium counterparts, continuously dissipate energy into their physical surroundings leading to entropy production and time-reversal symmetry breaking. This Letter discusses these issues in the context of quantum impurity models. We use simple thermodynamic arguments to define the rate of entropy production sigma and show that sigma has a simple information-theoretic interpretation in terms of nonequilibrium distribution functions. This allows us to show that the entropy production is strictly positive for any nonequilibrium steady state. We conclude by applying these ideas to the resonance level model and the Kondo model.     

Universal scaling of the conductivity at the superfluid-insulator phase transition

The scaling of the conductivity at the superfluid-insulator quantum phase transition in two dimensions is studied by numerical simulations of the Bose-Hubbard model. In contrast to previous studies, we focus on properties of this model in the experimentally relevant thermodynamic limit at finite temperature T. We find clear evidence for deviations from omega k scaling of the conductivity towards omega k/T scaling at low Matsubara frequencies omega k. By careful analytic continuation using Padé approximants we show that this behavior carries over to the real frequency axis where the conductivity scales with omega/T at small frequencies and low temperatures. We estimate the universal dc conductivity to be sigma* = 0.45(5)Q2/h, distinct from previous estimates in the T = 0, omega/T > 1 limit.     

Tunneling, dissipation, and superfluid transition in quantum Hall bilayers

We study bilayer quantum Hall systems at total Landau level filling factor nu=1 in the presence of interlayer tunneling and coupling to a dissipative normal fluid. Describing the dynamics of the interlayer phase by an effective quantum dissipative XY model, we show that there exists a critical dissipation sigma(c) set by the conductance of the normal fluid. For sigma>sigma(c), interlayer tunnel splitting drives the system to a nu=1 quantum Hall state. For sigma相似文献   

Modular invariance,universality and crossover in the quantum Hall effect

An analytic form for the conductivity tensor in crossover between two quantum Hall plateaux is derived, which appears to be in good agreement with existing experimental data. The derivation relies on an assumed symmetry between quantum Hall states, a generalisation of the law of corresponding states from rational filling factors to complex conductivity, which has a mathematical expression in terms of an action of the modular group on the upper-half complex conductivity plane. This symmetry implies universality in quantum Hall crossovers. The assumption that the β-function for the complex conductivity is a complex analytic function, together with some experimental constraints, results in an analytic expression for the crossover, as a function of the external magnetic field.     

Meson Properties at Finite Temperature in the Linear Sigma Model

The meson masses are investigated at finite temperature in the framework of the linear sigma model with an explicit chiral symmetry breaking term. The imaginary-time thermo-field dynamics and effective potential have been used for the calculation of the meson masses. We found that the behavior of the sigma and pion masses at finite temperature is in agreement with previous works. The critical temperature, the order of the phase transition, and the dependence of the meson fields on the temperature are discussed.     

Noncommutative linear sigma models

We examine noncommutative linear sigma models with U(N) global symmetry groups at the one-loop quantum level, and contrast the results with our previous study of the noncommutative O(N) linear sigma models where we have shown that Nambu–Goldstone symmetry realization is inconsistent with continuum renormalization. Specifically we find no violation of Goldstone's theorem at one-loop for the U(N) models with the quartic term ordering consistent with possible noncommutative gauging of the model. The difference is due to terms involving noncommutative commutator interactions, which vanish in the commutative limit. We also examine the U(2), and O(4) linear sigma models with matter in the adjoint representation, and find that the former is consistent with Goldstone's theorem at one-loop if we include only trace invariants consistent with possible noncommutative gauging of the model, while the latter exhibits violations of Goldstone's theorem of the kind seen in the fundamental of O(N) for N>2.     

A diagram technique for perturbation theory calculations of the effective conductivity of two-dimensional systems

The perturbation theory for calculating the ffective conductivity of the plane consisting of pieces of different conductivities is constructed, and a convenient diagram technique is elaborated for this perturbation theory. It is shown that for the chessboard, perturbative calculations give results that are in agreement with the well-known formula $\sigma _{eff} = \sqrt {\sigma _1 \sigma _2 } $ . The components of the effective conductivity tensor for the anisotropic three-color chessboard are calculated. It is shown that the isotropic (symmetric) part of the effective conductivity calculated up to the sixth order of perturbation theory satisfies the Bruggeman effective medium equation for symmetric three-color structures with equally partitioned components. We also consider an isotropic three-color chessboard with nonequal weights of colors. In this case, the perturbation theory in the fourth order contradicts the results following from the Bruggeman equation for nonequal weights.     

Stochastic field theory for a dirac particle propagating in gauge field disorder

Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four-dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white-noise potential, the gauge field disorder. Effective supersymmetric nonlinear sigma models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy within our generic model implying the universality of this scale in QCD. Connections to other low energy effective theories, in particular, the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.     

On the QCD phase structure from effective models

Some recent theoretical developments of the QCD phase diagram are summarized. Chiral symmetry restoration and the confinement/deconfinement transition at nonzero temperature and quark densities are analyzed in the framework of an effective linear sigma model with three light quark flavors. The sensitivity of the chiral transition as well as the existence of a critical end point in the phase diagram on the value of the sigma mass is explored. The influence of the axial anomaly on the chiral critical surface is addressed. Finally, the modifications by the inclusion of the Polyakov loop on the phase structure are investigated.