Integer quantum Hall effect and Hofstadter's butterfly spectra in three-dimensional metals in external periodic modulations

We propose that Hofstadter's butterfly accompanied by quantum Hall effect that is similar to those predicted to occur in 3D tight-binding systems by Koshino {\it et al.} [Phys. Rev. Lett. {\bf 86}, 1062 (2001)] can be realized in an entirely different system -- 3D metals applied with weak external periodic modulations (e.g., acoustic waves). Namely, an effect of two periodic potentials interferes with Landau's quantization due to an applied magnetic field \Vec{B}, resulting generally in fractal energy gaps as a function of the tilting angle of \Vec{B}, for which the accompanying quantized Hall tensors are computed. The phenomenon arises from the fact that, while the present system has a different physical origin for the butterfly from the 3D tight-binding systems, the mathematical forms are remarkably equivalent.Comment: 4 pages, 2 figure

Duality and integer quantum Hall effect in isotropic 3D crystals

We show here a series of energy gaps as in Hofstadter's butterfly, which have been shown to exist by Koshino et al [Phys. Rev. Lett. 86, 1062 (2001)] for anisotropic three-dimensional (3D) periodic systems in magnetic fields \Vec{B}, also arise in the isotropic case unless \Vec{B} points in high-symmetry directions. Accompanying integer quantum Hall conductivities $(\sigma_{xy}, \sigma_{yz}, \sigma_{zx})$ can, surprisingly, take values $\propto (1,0,0), (0,1,0), (0,0,1)$ even for a fixed direction of \Vec{B} unlike in the anisotropic case. We can intuitively explain the high-magnetic field spectra and the 3D QHE in terms of quantum mechanical hopping by introducing a ``duality'', which connects the 3D system in a strong \Vec{B} with another problem in a weak magnetic field $(\propto 1/B)$.Comment: 7 pages, 6 figure

Phase Diagram for the Hofstadter butterfly and integer quantum Hall effect in three dimensions

We give a perspective on the Hofstadter butterfly (fractal energy spectrum in magnetic fields), which we have shown to arise specifically in three-dimensional(3D) systems in our previous work. (i) We first obtain the `phase diagram' on a parameter space of the transfer energies and the magnetic field for the appearance of Hofstadter's butterfly spectrum in anisotropic crystals in 3D. (ii) We show that the orientation of the external magnetic field can be arbitrary to have the 3D butterfly. (iii) We show that the butterfly is beyond the semiclassical description. (iv) The required magnetic field for a representative organic metal is estimated to be modest ($\sim 40$ T) if we adopt higher Landau levels for the butterfly. (v) We give a simpler way of deriving the topological invariants that represent the quantum Hall numbers (i.e., two Hall conductivity in 3D, $\sigma_{xy}, \sigma_{zx}$, in units of $e^2/h$).Comment: 8 pages, 8 figures, eps versions of the figures will be sent on request to [email protected]

Conductance of tubular nanowires with disorder

We calculate the conductance of tubular-shaped nanowires having many potential scatterers at random positions. Our approach is based on the scattering matrix formalism and our results analyzed within the scaling theory of disordered conductors. When increasing the energy the conductance for a big enough number of impurities in the tube manifests a systematic evolution from the localized to the metallic regimes. Nevertheless, a conspicuous drop in conductance is predicted whenever a new transverse channel is open. Comparison with the semiclassical calculation leading to purely ohmic behavior is made.Comment: 8 pages, 5 figure

Graph products of spheres, associative graded algebras and Hilbert series

Given a finite, simple, vertex-weighted graph, we construct a graded associative (non-commutative) algebra, whose generators correspond to vertices and whose ideal of relations has generators that are graded commutators corresponding to edges. We show that the Hilbert series of this algebra is the inverse of the clique polynomial of the graph. Using this result it easy to recognize if the ideal is inert, from which strong results on the algebra follow. Non-commutative Grobner bases play an important role in our proof. There is an interesting application to toric topology. This algebra arises naturally from a partial product of spheres, which is a special case of a generalized moment-angle complex. We apply our result to the loop-space homology of this space.Comment: 19 pages, v3: elaborated on connections to related work, added more citations, to appear in Mathematische Zeitschrif

Integer quantum Hall effect for hard-core bosons and a failure of bosonic Chern-Simons mean-field theories for electrons at half-filled Landau level

Field-theoretical methods have been shown to be useful in constructing simple effective theories for two-dimensional (2D) systems. These effective theories are usually studied by perturbing around a mean-field approximation, so the question whether such an approximation is meaningful arises immediately. We here study 2D interacting electrons in a half-filled Landau level mapped onto interacting hard-core bosons in a magnetic field. We argue that an interacting hard-core boson system in a uniform external field such that there is one flux quantum per particle (unit filling) exhibits an integer quantum Hall effect. As a consequence, the mean-field approximation for mapping electrons at half-filling to a boson system at integer filling fails.Comment: 13 pages latex with revtex. To be published in Phys. Rev.

Finite Size and Current Effects on IV Characteristics of Josephson Junction Arrays

The effects of finite size and of finite current on the current-voltage characteristics of Josephson junction arrays is studied both theoretically and by numerical simulations. The cross-over from non-linear to linear behavior at low temperature is shown to be a finite size effect and the non-linear behavior at higher temperature, $T>T_{KT}$, is shown to be a finite current effect. These are argued to result from competition between the three length scales characterizing the system. The importance of boundary effects is discussed and it is shown that these may dominate the behavior in small arrays.Comment: 5 pages, figures included, to appear in PR

Early Stages of Homopolymer Collapse

Interest in the protein folding problem has motivated a wide range of theoretical and experimental studies of the kinetics of the collapse of flexible homopolymers. In this Paper a phenomenological model is proposed for the kinetics of the early stages of homopolymer collapse following a quench from temperatures above to below the theta temperature. In the first stage, nascent droplets of the dense phase are formed, with little effect on the configurations of the bridges that join them. The droplets then grow by accreting monomers from the bridges, thus causing the bridges to stretch. During these two stages the overall dimensions of the chain decrease only weakly. Further growth of the droplets is accomplished by the shortening of the bridges, which causes the shrinking of the overall dimensions of the chain. The characteristic times of the three stages respectively scale as the zeroth, 1/5 and 6/5 power of the the degree of polymerization of the chain.Comment: 11 pages, 3 figure

Higher Order Effects in the Dielectric Constant of Percolative Metal-Insulator Systems above the Critical Point

The dielectric constant of a conductor-insulator mixture shows a pronounced maximum above the critical volume concentration. Further experimental evidence is presented as well as a theoretical consideration based on a phenomenological equation. Explicit expressions are given for the position of the maximum in terms of scaling parameters and the (complex) conductances of the conductor and insulator. In order to fit some of the data, a volume fraction dependent expression for the conductivity of the more highly conductive component is introduced.Comment: 4 pages, Latex, 4 postscript (*.epsi) files submitted to Phys Rev.

Fluctuation Relations for Diffusion Processes

The paper presents a unified approach to different fluctuation relations for classical nonequilibrium dynamics described by diffusion processes. Such relations compare the statistics of fluctuations of the entropy production or work in the original process to the similar statistics in the time-reversed process. The origin of a variety of fluctuation relations is traced to the use of different time reversals. It is also shown how the application of the presented approach to the tangent process describing the joint evolution of infinitesimally close trajectories of the original process leads to a multiplicative extension of the fluctuation relations.Comment: 38 page