Electron transport in strongly disordered structures

Using the transfer matrix technique, we investigate the propagation of electron through a two dimensional disordered sample. We find that the spatial distribution of electrons is homogeneous only in the limit of weak disorder (diffusive transport regime). In the limit of very strong disorder, we identify a narrow channel through which the electron propagates from one side of the sample to the opposite side. Even in this limit, we prove the wave character of the electron propagation.Comment: Presented at ETOPIM

Probability distribution of the conductance at the mobility edge

Distribution of the conductance P(g) at the critical point of the metal-insulator transition is presented for three and four dimensional orthogonal systems. The form of the distribution is discussed. Dimension dependence of P(g) is proven. The limiting cases $g\to\infty$ and $g\to 0$ are discussed in detail and relation $P(g)\to 0$ in the limit $g\to 0$ is proven.Comment: 4 pages, 3 .eps figure

Comment on the paper I. M. Suslov: Finite Size Scaling from the Self Consistent Theory of Localization

In the recent paper [I.M.Suslov, JETP {\bf 114} (2012) 107] a new scaling theory of electron localization was proposed. We show that numerical data for the quasi-one dimensional Anderson model do not support predictions of this theory.Comment: Comment on the paper arXiv 1104.043

Critical conductance of the chiral 2d random flux model

The two-terminal conductance of a random flux model defined on a square lattice is investigated numerically at the band center using a transfer matrix method. Due to the chiral symmetry, there exists a critical point where the ensemble averaged mean conductance is scale independent. We also study the conductance distribution function which depends on the boundary conditions and on the number of lattice sites being even or odd. We derive a critical exponent $\nu=0.42\pm 0.05$ for square samples of even width using one-parameter scaling of the conductance. This result could not be obtained previously from the divergence of the localization length in quasi-one-dimensional systems due to pronounced finite-size effects.Comment: EP2DS-17, Genua 2007, accepted for publication in Physica

Disordered two-dimensional electron systems with chiral symmetry

We review the results of our recent numerical investigations on the electronic properties of disordered two dimensional systems with chiral unitary, chiral orthogonal, and chiral symplectic symmetry. Of particular interest is the behavior of the density of states and the logarithmic scaling of the smallest Lyapunov exponents in the vicinity of the chiral quantum critical point in the band center at E=0. The observed peaks or depressions in the density of states, the distribution of the critical conductances, and the possible non-universality of the critical exponents for certain chiral unitary models are discussed

Symmetry, dimension and the distribution of the conductance at the mobility edge

The probability distribution of the conductance at the mobility edge, $p_c(g)$, in different universality classes and dimensions is investigated numerically for a variety of random systems. It is shown that $p_c(g)$ is universal for systems of given symmetry, dimensionality, and boundary conditions. An analytical form of $p_c(g)$ for small values of $g$ is discussed and agreement with numerical data is observed. For $g > 1$, $\ln p_c(g)$ is proportional to $(g-1)$ rather than $(g-1)^2$.Comment: 4 pages REVTeX, 5 figures and 2 tables include

Absorption losses in periodic arrays of thin metallic wires

We analyze the transmission and reflection of the electromagnetic wave calculated from transfer matrix simulations of periodic arrangements of thin metallic wires. The effective permittivity and the absorption is determined. Their dependence on the wire thickness and the conductance of the metallic wires is studied. The cutoff frequency or effective plasma frequency is obtained and is compared with analytical predictions. It is shown that the periodic arrangement of wires exhibits a frequency region in which the real part of the permittivity is negative while its imaginary part is very small. This behavior is seen for wires with thickness as small as 17 $\mu$m with a lattice constant of 3.33 mm

Reconciling Conductance Fluctuations and the Scaling Theory of Localization

We reconcile the phenomenon of mesoscopic conductance fluctuations with the single parameter scaling theory of the Anderson transition. We calculate three averages of the conductance distribution: $\exp()$, $$ and $1/$ where $g$ is the conductance in units of $e^2/h$ and $R=1/g$ is the resistance and demonstrate that these quantities obey single parameter scaling laws. We obtain consistent estimates of the critical exponent from the scaling of all these quantities

Resonant and anti-resonant frequency dependence of the effective parameters of metamaterials

We present a numerical study of the electromagnetic response of the metamaterial elements that are usedto construct materials with negative refractive index. For an array of split ring resonators (SRR) we find that the resonant behavior of the effective magnetic permeability is accompanied by an anti-resonant behavior of the effective permittivity. In addition, the imaginary parts of the effective permittivity and permeability are opposite in sign. We also observe an identical resonant versus anti-resonant frequency dependence of the effective materials parameters for a periodic array of thin metallic wires with cuts placed periodically along the length of the wire, with roles of the permittivity and permeability reversed from the SRR case. We show in a simple manner that the finite unit cell size is responsible for the anti-resonant behavior

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