Critical conductance of two-dimensional chiral systems with random magnetic flux

The zero temperature transport properties of two-dimensional lattice systems with static random magnetic flux per plaquette and zero mean are investigated numerically. We study the two-terminal conductance and its dependence on energy, sample size, and magnetic flux strength. The influence of boundary conditions and of the oddness of the number of sites in the transverse direction is also studied. We confirm the existence of a critical chiral state in the middle of the energy band and calculate the critical exponent nu=0.35 +/- 0.03 for the divergence of the localization length. The sample averaged scale independent critical conductance _c turns out to be a function of the amplitude of the flux fluctuations whereas the variance of the respective conductance distributions appears to be universal. All electronic states outside of the band center are found to be localized.Comment: to appear in Phys. Rev.

Boundary hopping and the mobility edge in the Anderson model in three dimensions

It is shown, using high-precision numerical simulations, that the mobility edge of the 3d Anderson model depends on the boundary hopping term t in the infinite size limit. The critical exponent is independent of it. The renormalized localization length at the critical point is also found to depend on t but not on the distribution of on-site energies for box and Lorentzian distributions. Implications of results for the description of the transition in terms of a local order-parameter are discussed

Weak disorder expansion for localization lengths of quasi-1D systems

A perturbative formula for the lowest Lyapunov exponent of an Anderson model on a strip is presented. It is expressed in terms of an energy-dependent doubly stochastic matrix, the size of which is proportional to the strip width. This matrix and the resulting perturbative expression for the Lyapunov exponent are evaluated numerically. Dependence on energy, strip width and disorder strength are thoroughly compared with the results obtained by the standard transfer matrix method. Good agreement is found for all energies in the band of the free operator and this even for quite large values of the disorder strength

Localizations in coupled electronic chains

We studied effects of random potentials and roles of electron-electron interactions in the gapless phase of coupled Hubbard chains, using a renormalization group technique. For non-interacting electrons, we obtained the localization length proportional to the number of chains, as already shown in the other approaches. For interacting electrons, the localization length is longer for stronger interactions, that is, the interactions counteract the random potentials. Accordingly, the localization length is not a simple linear function of the number of chains. This interaction effect is strongest when there is only a single chain. We also calculate the effects of interactions and random potentials on charge stiffness.Comment: no figure, to appear in Phys. Rev.

Strongly correlated wave functions for artificial atoms and molecules

A method for constructing semianalytical strongly correlated wave functions for single and molecular quantum dots is presented. It employs a two-step approach of symmetry breaking at the Hartree-Fock level and of subsequent restoration of total spin and angular momentum symmetries via Projection Techniques. Illustrative applications are presented for the case of a two-electron helium-like single quantum dot and a hydrogen-like quantum dot molecule.Comment: 9 pages. Revtex with 2 GIF and 1 EPS figures. Published version with extensive clarifications. A version of the manuscript with high quality figures incorporated in the text is available at http://calcite.physics.gatech.edu/~costas/qdhelproj.html For related papers, see http://www.prism.gatech.edu/~ph274c

Conductance Correlations Near Integer Quantum Hall Transitions

In a disordered mesoscopic system, the typical spacing between the peaks and the valleys of the conductance as a function of Fermi energy $E_F$ is called the conductance energy correlation range $E_c$. Under the ergodic hypothesis, the latter is determined by the half-width of the ensemble averaged conductance correlation function: $F=$. In ordinary diffusive metals, $E_c\sim D/L^2$, where $D$ is the diffusion constant and $L$ is the linear dimension of the phase-coherent sample. However, near a quantum phase transition driven by the location of the Fermi energy $E_F$, the above picture breaks down. As an example of the latter, we study, for the first time, the conductance correlations near the integer quantum Hall transitions of which $E_F$ is a critical coupling constant. We point out that the behavior of $F$ is determined by the interplay between the static and the dynamic properties of the critical phenomena.Comment: 4 pages, 4 figures, minor corrections, to appear in Phys. Rev. Let

Effects of Scale-Free Disorder on the Anderson Metal-Insulator Transition

We investigate the three-dimensional Anderson model of localization via a modified transfer-matrix method in the presence of scale-free diagonal disorder characterized by a disorder correlation function $g(r)$ decaying asymptotically as $r^{-\alpha}$. We study the dependence of the localization-length exponent $\nu$ on the correlation-strength exponent $\alpha$. % For fixed disorder $W$, there is a critical $\alpha_{\rm c}$, such that for $\alpha < \alpha_{\rm c}$, $\nu=2/\alpha$ and for $\alpha > \alpha_{\rm c}$, $\nu$ remains that of the uncorrelated system in accordance with the extended Harris criterion. At the band center, $\nu$ is independent of $\alpha$ but equal to that of the uncorrelated system. The physical mechanisms leading to this different behavior are discussed.Comment: submitted to Phys. Rev. Let

The Anderson Transition in Two-Dimensional Systems with Spin-Orbit Coupling

We report a numerical investigation of the Anderson transition in two-dimensional systems with spin-orbit coupling. An accurate estimate of the critical exponent $\nu$ for the divergence of the localization length in this universality class has to our knowledge not been reported in the literature. Here we analyse the SU(2) model. We find that for this model corrections to scaling due to irrelevant scaling variables may be neglected permitting an accurate estimate of the exponent $\nu=2.73 \pm 0.02$

Electronic transport in strongly anisotropic disordered systems: model for the random matrix theory with non-integer beta

We study numerically an electronic transport in strongly anisotropic weakly disorderd two-dimensional systems. We find that the conductance distribution is gaussian but the conductance fluctuations increase when anisotropy becomes stronger. We interpret this result by random matrix theory with non-integer symmetry parameter beta, in accordance with recent theoretical work of K.A.Muttalib and J.R.Klauder [Phys.Rev.Lett. 82 (1999) 4272]. Analysis of the statistics of transport paramateres supports this hypothesis.Comment: 8 pages, 7 *.eps figure

Multifractality of the quantum Hall wave functions in higher Landau levels

To probe the universality class of the quantum Hall system at the metal-insulator critical point, the multifractality of the wave function $\psi$ is studied for higher Landau levels, $N=1,2$, for various range $(\sigma )$ of random potential. We have found that, while the multifractal spectrum $f(\alpha)$ (and consequently the fractal dimension) does vary with $N$, the parabolic form for $f(\alpha)$ indicative of a log-normal distribution of $\psi$ persists in higher Landau levels. If we relate the multifractality with the scaling of localization via the conformal theory, an asymptotic recovery of the single-parameter scaling with increasing $\sigma$ is seen, in agreement with Huckestein's irrelevant scaling field argument.Comment: 10 pages, revtex, 5 figures available on request from [email protected]