Transport between edge states in multilayer integer quantum Hall systems: exact treatment of Coulomb interactions and disorder

A set of stacked two-dimensional electron systems in a perpendicular magnetic field exhibits a three-dimensional version of the quantum Hall effect if interlayer tunneling is not too strong. When such a sample is in a quantum Hall plateau, the edge states of each layer combine to form a chiral metal at the sample surface. We study the interplay of interactions and disorder in transport properties of the chiral metal, in the regime of weak interlayer tunneling. Our starting point is a system without interlayer tunneling, in which the only excitations are harmonic collective modes: surface magnetoplasmons. Using bosonization and working perturbatively in the interlayer tunneling amplitude, we express transport properties in terms of the spectrum for these collective modes, treating electron-electron interactions and impurity scattering exactly. We calculte the conductivity as a function of temperature, finding that it increases with increasing temperature as observed in recent experiments. We also calculate the autocorrelation function of mesoscopic conductance fluctuations induced by changes in a magnetic field component perpendicular to the sample surface, and its dependence on temperature. We show that conductance fluctuations are characterised by a dephasing length that varies inversely with temperature.Comment: 13 pages, 10 figures, minor changes made for publicatio

The fractional quantum Hall effect in infinite layer systems

Stacked two dimensional electron systems in transverse magnetic fields exhibit three dimensional fractional quantum Hall phases. We analyze the simplest such phases and find novel bulk properties, e.g., irrational braiding. These phases host ``one and a half'' dimensional surface phases in which motion in one direction is chiral. We offer a general analysis of conduction in the latter by combining sum rule and renormalization group arguments, and find that when interlayer tunneling is marginal or irrelevant they are chiral semi-metals that conduct only at T > 0 or with disorder.Comment: RevTeX 3.0, 4p., 2 figs with epsf; reference to the detailed companion paper cond-mat/0006506 adde

Metal-insulator transition in a multilayer system with a strong magnetic field

We study the Anderson localization in a weakly coupled multilayer system with a strong magnetic field perpendicular to the layers. The phase diagram of 1/3 flux quanta per plaquette is obtained. The phase diagram shows that a three-dimensional quantum Hall effect phase exists for a weak on-site disorder. For intermediate disorder, the system has insulating and normal metallic phases separated by a mobility edge. At an even larger disorder, all states are localized and the system is an insulator. The critical exponent of the localization length is found to be $\nu=1.57\pm0.10$.Comment: Latex file, 3 figure

The transverse magnetoresistance of the two-dimensional chiral metal

We consider the two-dimensional chiral metal, which exists at the surface of a layered, three-dimensional sample exhibiting the integer quantum Hall effect. We calculate its magnetoresistance in response to a component of magnetic field perpendicular to the sample surface, in the low temperature, but macroscopic, regime where inelastic scattering may be neglected. The magnetoresistance is positive, following a Drude form with a field scale, $B_0=\Phi_0/al_{\text{el}}$, given by the transverse field strength at which one quantum of flux, $\Phi_0$, passes through a rectangle with sides set by the layer-spacing, $a$, and the elastic mean free path, $l_{\text{el}}$. Experimental measurement of this magnetoresistance may therefore provide a direct determination of the elastic mean free path in the chiral metal.Comment: submitted to Phys Rev

Dynamics and Critical Behaviour of the q-model

The $q$-model, a random walk model rich in behaviour and applications, is investigated. We introduce and motivate the $q$-model via its application proposed by Coppersmith {\em et al.} to the flow of stress through granular matter at rest. For a special value of its parameters the $q$-model has a critical point that we analyse. To characterise the critical point we imagine that a uniform load has been applied to the top of the granular medium and we study the evolution with depth of fluctuations in the distribution of load. Close to the critical point explicit calculation reveals that the evolution of load exhibits scaling behaviour analogous to thermodynamic critical phenomena. The critical behaviour is remarkably tractable: the harvest of analytic results includes scaling functions that describe the evolution of the variance of the load distribution close to the critical point and of the entire load distribution right at the critical point, values of the associated critical exponents, and determination of the upper critical dimension. These results are of intrinsic interest as a tractable example of a random critical point. Of the many applications of the q-model, the critical behaviour is particularly relevant to network models of river basins, as we briefly discuss. Finally we discuss circumstances under which quantum network models that describe the surface electronic states of a quantum Hall multilayer can be mapped onto the classical $q$-model. For mesoscopic multilayers of finite circumference the mapping fails; instead a mapping to a ferromagnetic supersymmetric spin chain has proved fruitful. We discuss aspects of the superspin mapping and give a new elementary derivation of it making use of operator rather than functional methods.Comment: 34 pages, Revtex, typo correcte

Thermal activation between Landau levels in the organic superconductor β′′\beta''-(BEDT-TTF)2_{2}SF5_{5}CH2_{2}CF2_{2}SO3_{3}

We show that Shubnikov-de Haas oscillations in the interlayer resistivity of the organic superconductor $\beta''$-(BEDT-TTF)$_{2}$SF$_{5}$ CH$_{2}$CF$_{2}$SO$_{3}$ become very pronounced in magnetic fields $\sim$~60~T. The conductivity minima exhibit thermally-activated behaviour that can be explained simply by the presence of a Landau gap, with the quasi-one-dimensional Fermi surface sheets contributing negligibly to the conductivity. This observation, together with complete suppression of chemical potential oscillations, is consistent with an incommensurate nesting instability of the quasi-one-dimensional sheets.Comment: 6 pages, 4 figure

Are Directed Waves Multifractal?

Wave propagation is studied in a sufficiently anisotropic random medium that backscattering along one direction can be neglected. A Fokker-Planck equation is derived the solution to which would provide a complete statistical description of such directed waves. The Fokker-Planck equation is mapped onto an su(1,1) ferromagnet and its symmetries are identified. Using the symmetries asymptotic wave function distributions are computed and used to show that directed wave functions fill space uniformly and do not have multifractal character.Comment: 5 pages. Submitted to Phys Rev Let

Quantum Hall Effect in Three Dimensional Layered Systems

Using a mapping of a layered three-dimensional system with significant inter-layer tunneling onto a spin-Hamiltonian, the phase diagram in the strong magnetic field limit is obtained in the semi-classical approximation. This phase diagram, which exhibit a metallic phase for a finite range of energies and magnetic fields, and the calculated associated critical exponent, $\nu=4/3$, agree excellently with existing numerical calculations. The implication of this work for the quantum Hall effect in three dimensions is discussed.Comment: 4 pages + 4 figure

Edge electron states for quasi-one-dimensional organic conductors in the magnetic-field-induced spin-density-wave phases

We develop a microscopic picture of the electron states localized at the edges perpendicular to the chains in the Bechgaard salts in the quantum Hall regime. In a magnetic-field-induced spin-density-wave state (FISDW) characterized by an integer N, there exist N branches of chiral gapless edge excitations. Localization length is much longer and velocity much lower for these states than for the edge states parallel to the chains. We calculate the contribution of these states to the specific heat and propose a time-of-flight experiment to probe the propagating edge modes directly.Comment: 4 pages, 2 figures. V.2: Minor changes to the final version published in PR

Critical State Behaviour in a Low Dimensional Metal Induced by Strong Magnetic Fields

We present the results of magnetotransport and magnetic torque measurements on the alpha-(BEDT-TTF)2KHg(SCN)4 charge-transfer salt within the high magnetic field phase, in magnetic fields extending to 33 T and temperatures as low as 27 mK. While the high magnetic field phase (at fields greater than ~ 23 T) is expected, on theoretical grounds, to be either a modulated charge-density wave phase or a charge/spin-density wave hybrid, the resistivity undergoes a dramatic drop below ~ 3 K within the high magnetic field phase, falling in an approximately exponential fashion at low temperatures, while the magnetic torque exhibits pronounced hysteresis effects. This hysteresis, which occurs over a broad range of fields, is both strongly temperature-dependent and has several of the behavioural characteristics predicted by critical-state models used to describe the pinning of vortices in type II superconductors in strong magnetic fields. Thus, rather than exhibiting the usual behaviour expected for a density wave ground state, both the transport and the magnetic properties of alpha-(BEDT-TTF)2KHg(SCN)4, at high magnetic fields, closely resembles those of a type II superconductor