Integer Quantum Hall Effect for Lattice Fermions

A two-dimensional lattice model for non-interacting fermions in a magnetic field with half a flux quantum per plaquette and $N$ levels per site is considered. This is a model which exhibits the Integer Quantum Hall Effect (IQHE) in the presence of disorder. It presents an alternative to the continuous picture for the IQHE with Landau levels. The large $N$ limit can be solved: two Hall transitions appear and there is an interpolating behavior between the two Hall plateaux. Although this approach to the IQHE is different from the traditional one with Landau levels because of different symmetries (continuous for Landau levels and discrete here), some characteristic features are reproduced. For instance, the slope of the Hall conductivity is infinite at the transition points and the electronic states are delocalized only at the transitions.Comment: 9 pages, Plain-Te

Hall Resistivity and Dephasing in the Quantum Hall Insulator

The longstanding problem of the Hall resistivity rho(x,y) in the Hall insulator phase is addressed using four-lead Chalker-Coddington networks. Electron interaction effects are introduced via a finite dephasing length. In the quantum coherent regime, we find that rho(x,y) scales with the longitudinal resistivity rho(x,x), and they both diverge exponentially with dephasing length. In the Ohmic limit, (dephasing length shorter than Hall puddles' size), rho(x,y) remains quantized and independent of rho(x,x). This suggests a new experimental probe for dephasing processes.Comment: RevTeX, 4 pages, 3 figures included with epsf.st

On the Relevance of Disorder for Dirac Fermions with Imaginary Vector Potential

We consider the effects of disorder in a Dirac-like Hamiltonian. In order to use conformal perturbation theory, we argue that one should consider disorder in an imaginary vector potential. This affects significantly the signs of the lowest order $\beta$eta functions. We present evidence for the existence of two distinct universality classes, depending on the relative strengths of the gauge field verses impurity disorder strengths. In one class all disorder is driven irrelevant by the gauge field disorder.Comment: 4 pages, 1 figure. New version has expanded and improved discussion of why one should consider an imaginary vector potential in a physical localization problem. Factors of 2 in beta functions corrected. References adde

Universal Scaling of Strong-Field Localization in an Integer Quantum Hall Liquid

We study the Landau level localization and scaling properties of a disordered two-dimensional electron gas in the presence of a strong external magnetic field. The impurities are treated as random distributed scattering centers with parameterized potentials. Using a transfer matrix for a finite-width strip geometry, we calculate the localization length as a function of system size and electron energy. The finite-size localization length is determined by calculating the Lyapunov exponents of the transfer matrix. A detailed finite-size scaling analysis is used to study the critical behavior near the center of the Landau bands. The influence of varying the impurity concentration, the scattering potential range and its nature, and the Landau level index on the scaling behavior and on the critical exponent is systematically investigated. Particular emphasis is put on studying the effects of finite range of the disorder potential and Landau level coupling on the quantum localization behavior. Our numerical results, which are carried out on systems much larger than those studied before, indicate that pure $\delta$-function disorder in the absence of any Landau level coupling gives rise to non-universal localization properties with the critical exponents in the lowest two Landau levels being substantially different. Inclusion of a finite potential range and/or Landau level mixing may be essential in producing universality in the localization.Comment: 28 pages, Latex, 17 figures (available upon request), #phd0

Duality and Universality for the Chern-Simons bosons

By mapping the relativistic version of the Chern-Simons-Landau-Ginzburg theory in 2+1 dimensions to the 3D lattice Villain x-y model coupled with the Chern-Simons gauge field, we investigate phase transitions of Chern-Simons bosons in the limit of strong coupling. We construct algebraically exact duality and flux attachment transformations of the lattice theories, corresponding to analogous transformations in the continuum limit. These transformations are used to convert the model with arbitrary fractional Chern-Simons coefficient $\alpha$ to a model with $\alpha$ either zero or one. Depending on this final value of $\alpha$, the phase transition in the original model is either in the universality class of the 3D x-y model or a ``fermionic'' universality class, unless the irrelevant corrections of cubic and higher power in momenta render the transition of the first order.Comment: 14 two-column pages, revtex 3.0, multicol and epsf.sty (optional), one PostScript figure, Submitted to Phys. Rev. B The changes intended to simplify the arguments and eliminate logical gaps. We also show how the filling factor $\nu$ is changed by the duality transformatio

Integer Quantum Hall Effect in Double-Layer Systems

We consider the localization of independent electron orbitals in double-layer two-dimensional electron systems in the strong magnetic field limit. Our study is based on numerical Thouless number calculations for realistic microscopic models and on transfer matrix calculations for phenomenological network models. The microscopic calculations indicate a crossover regime for weak interlayer tunneling in which the correlation length exponent appears to increase. Comparison of network model calculations with microscopic calculations casts doubt on their generic applicability.Comment: 14 pages, 12 figures included, RevTeX 3.0 and epsf. Additional reference

The Molecular Diversity of Freshwater Picoeukaryotes Reveals High Occurrence of Putative Parasitoids in the Plankton

Eukaryotic microorganisms have been undersampled in biodiversity studies in freshwater environments. We present an original 18S rDNA survey of freshwater picoeukaryotes sampled during spring/summer 2005, complementing an earlier study conducted in autumn 2004 in Lake Pavin (France). These studies were designed to detect the small unidentified heterotrophic flagellates (HF, 0.6–5 µm) which are considered the main bacterivores in aquatic systems. Alveolates, Fungi and Stramenopiles represented 65% of the total diversity and differed from the dominant groups known from microscopic studies. Fungi and Telonemia taxa were restricted to the oxic zone which displayed two fold more operational taxonomic units (OTUs) than the oxycline. Temporal forcing also appeared as a driving force in the diversification within targeted organisms. Several sequences were not similar to those in databases and were considered as new or unsampled taxa, some of which may be typical of freshwater environments. Two taxa known from marine systems, the genera Telonema and Amoebophrya, were retrieved for the first time in our freshwater study. The analysis of potential trophic strategies displayed among the targeted HF highlighted the dominance of parasites and saprotrophs, and provided indications that these organisms have probably been wrongfully regarded as bacterivores in previous studies. A theoretical exercise based on a new ‘parasite/saprotroph-dominated HF hypothesis’ demonstrates that the inclusion of parasites and saprotrophs may increase the functional role of the microbial loop as a link for carbon flows in pelagic ecosystems. New interesting perspectives in aquatic microbial ecology are thus opened

Scaling Theory of the Integer Quantum Hall Effect

The scaling theory of the transitions between plateaus of the Hall conductivity in the integer Quantum Hall effect is reviewed. In the model of two-dimensional noninteracting electrons in strong magnetic fields the transitions are disorder-induced localization-delocalization transitions. While experimental and analytical approaches are surveyed, the main emphasis is on numerical studies, which successfully describe the experiments. The theoretical models for disordered systems are described in detail. An overview of the finite-size scaling theory and its relation to Anderson localization is given. The field-theoretical approach to the localization problem is outlined. Numerical methods for the calculation of scaling quantities, in particular the localization length, are detailed. The properties of local observables at the localization-delocalization transition are discussed in terms of multifractal measures. Finally, the results of extensive numerical investigations are compared with experimental findings.Comment: 96 pages, REVTeX 3, 28 figures, Figs. 8-24, 26-28 appended as uuencoded compressed tarred PostScript files. Submitted to Rev. Mod. Phys