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]

Hopping electron model with geometrical frustration: kinetic Monte Carlo simulations

The hopping electron model on the Kagome lattice was investigated by kinetic Monte Carlo simulations, and the non-equilibrium nature of the system was studied. We have numerically confirmed that aging phenomena are present in the autocorrelation function \hbox{$C \, \left({t,t_{W} } \right)$} of the electron system on the Kagome lattice, which is a geometrically frustrated lattice without any disorder. The waiting-time distributions \hbox{$p\left(\tau \right)$} of hopping electrons of the system on Kagome lattice has been also studied. It is confirmed that the profile of \hbox{$p\, \left(\tau \right)$} obtained at lower temperatures obeys the power-law behavior, which is a characteristic feature of continuous time random walk of electrons. These features were also compared with the characteristics of the Coulomb glass model, used as a model of disordered thin films and doped semiconductors. This work represents an advance in the understanding of the dynamics of geometrically frustrated systems and will serve as a basis for further studies of these physical systems

Numerical methods for design of metamaterial photonic crystals and random metamaterials

Two-dimensional metamaterial photonic crystals (2DMPCs) composed of dispersive metamaterials in a positive-refractive-index medium were investigated by incorporating finite-difference time-domain calculations into the auxiliary differential equation method. A distinct band gap was formed and the effects of positional and size disorder when the dispersive metamaterials are aligned in air were elucidated. In addition, using the self-consistent finite-difference frequency-domain method, an eigenmode analysis of 2DMPCs with positional disorder was performed. Finally, a numerical method for the inverse design of binary random metamaterial multilayers was proposed