Quantum critical behaviour of the plateau-insulator transition in the quantum Hall regime

High-field magnetotransport experiments provide an excellent tool to investigate the plateau-insulator phase transition in the integral quantum Hall effect. Here we review recent low-temperature high-field magnetotransport studies carried out on several InGaAs/InP heterostructures and an InGaAs/GaAs quantum well. We find that the longitudinal resistivity $\rho_{xx}$ near the critical filling factor $\nu_{c}$ ~ 0.5 follows the universal scaling law $\rho_{xx}(\nu, T) \propto exp[-\Delta \nu/(T/T_{0})^{\kappa}]$, where $\Delta \nu =\nu -\nu_{c}$. The critical exponent $\kappa$ equals $0.56 \pm 0.02$, which indicates that the plateau-insulator transition falls in a non-Fermi liquid universality class.Comment: 8 pages, accepted for publication in Proceedings of the Yamada Conference LX on Research in High Magnetic Fields (August 16-19, 2006, Sendai

Single-particle and Interaction Effects on the Cohesion and Transport and Magnetic Properties of Metal Nanowires at Finite Voltages

The single-particle and interaction effects on the cohesion, electronic transport, and some magnetic properties of metallic nanocylinders have been studied at finite voltages by using a generalized mean-field electron model. The electron-electron interactions are treated in the self-consistent Hartree approximation. Our results show the single-particle effect is dominant in the cohesive force, while the nonzero magnetoconductance and magnetotension coefficients are attributed to the interaction effect. Both single-particle and interaction effects are important to the differential conductance and magnetic susceptibility.Comment: 5 pages, 6 figure

Alternative approach to computing transport coefficients: application to conductivity and Hall coefficient of hydrogenated amorphous silicon

We introduce a theoretical framework for computing transport coefficients for complex materials. As a first example, we resolve long-standing inconsistencies between experiment and theory pertaining to the conductivity and Hall mobility for amorphous silicon and show that the Hall sign anomaly is a consequence of localized states. Next, we compute the AC conductivity of amorphous polyanaline. The formalism is applicable to complex materials involving defects and band-tail states originating from static topological disorder and extended states. The method may be readily integrated with current \textit{ab initio} methods.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let

Momentum average approximation for models with boson-modulated hopping: Role of closed loops in the dynamical generation of a finite quasiparticle mass

We generalize the momentum average approximation to study the properties of single polarons in models with boson affected hopping, where the fermion-boson scattering depends explicitly on both the fermion's and the boson's momentum. As a specific example, we investigate the Edwards fermion-boson model in both one and two dimensions. In one dimension, this allows us to compare our results with exact diagonalization results, to validate the accuracy of our approximation. The generalization to two-dimensional lattices allows us to calculate the polaron's quasiparticle weight and dispersion throughout the Brillouin zone and to demonstrate the importance of Trugman loops in generating a finite effective mass even when the free fermion has an infinite mass.Comment: 15 pages, 14 figure

Determining ethylene group disorder levels in κ\kappa-(BEDT-TTF)2_2Cu[N(CN)2_2]Br

We present a detailed structural investigation of the organic superconductor $\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br at temperatures $T$ from 9 to 300 K. Anomalies in the $T$ dependence of the lattice parameters are associated with a glass-like transition previously reported at $T_g$ = 77 K. From structure refinements at 9, 100 and 300 K, the orthorhombic crystalline symmetry, space group {\it Pnma}, is established at all temperatures. Further, we extract the $T$ dependence of the occupation factor of the eclipsed conformation of the terminal ethylene groups of the BEDT-TTF molecule. At 300 K, we find 67(2) %, with an increase to 97(3) % at 9 K. We conclude that the glass-like transition is not primarily caused by configurational freezing-out of the ethylene groups

On the transcendence degree of the differential field generated by Siegel modular forms

It is a classical fact that the elliptic modular functions satisfies an algebraic differential equation of order 3, and none of lower order. We show how this generalizes to Siegel modular functions of arbitrary degree. The key idea is that the partial differential equations they satisfy are governed by Gauss--Manin connections, whose monodromy groups are well-known. Modular theta functions provide a concrete interpretation of our result, and we study their differential properties in detail in the case of degree 2.Comment: 21 pages, AmSTeX, uses picture.sty for 1 LaTeX picture; submitted for publicatio

The anomaly-free quantization of two-dimensional relativistic string. I

An anomaly-free quantum theory of a relativistic string is constructed in two-dimensional space-time. The states of the string are found to be similar to the states of a massless chiral quantum particle. This result is obtained by generalizing the concept of an ``operator'' in quantum field theory.Comment: LaTeX, 19 pages, no figure

Characteristic Potentials for Mesoscopic Rings Threaded by an Aharonov-Bohm Flux

Electro-static potentials for samples with the topology of a ring and penetrated by an Aharonov-Bohm flux are discussed. The sensitivity of the electron-density distribution to small variations in the flux generates an effective electro-static potential which is itself a periodic function of flux. We investigate a simple model in which the flux sensitive potential leads to a persistent current which is enhanced compared to that of a loop of non-interacting electrons. For sample geometries with contacts the sensitivity of the electro-static potential to flux leads to a flux-induced capacitance. This capacitance gives the variation in charge due to an increment in flux. The flux-induced capacitance is contrasted with the electro-chemical capacitance which gives the variation in charge due to an increment in an electro-chemical potential. The discussion is formulated in terms of characteristic functions which give the variation of the electro-static potential in the interior of the conductor due to an increment in the external control parameters (flux, electro-chemical potentials). Paper submitted to the 16th Nordic Semiconductor Meeting, Laugarvatan, Iceland, June 12-15, 1994. The proceedings will be published in Physica Scripta.Comment: 23 pages + 4 figures, revtex, IBM-RC1955