Anderson localization and propagation of electromagnetic waves through disordered media

We have used the dynamic method to calculate the frequency dependence of the localization length in a disordered medium, using the amplitude change and the redshift of the spectral density of the propagating incident pulse. The frequency dependence of the localization length in an effectively one-dimensional disordered medium is computed in terms of the strength of the disorder. The results obtained with the dynamic method are confirmed by computing the same results using the transfer-matrix method.     

Zero bias anomaly in tunnel resistance and electron-electron interaction

In this paper we consider the properties of the disordered systems, when the mean free path of electrons is more or comparable with its wave length, i.e. some higher the localization edge. It is shown that the electron-electron interaction in this situation leads to an anomaly in the density of states near the Fermi level. We argue that this anomaly causes that of the tunnel resistance. The minimum in the temperature dependence of the resistivity in the disordered metals may also be due to a similar mechanism.     

Enhanced resonant backscattering of excitons in disordered quantum wells

A clear signature of enhanced backscattering of excitons is observed in the directional resonant Rayleigh scattering of light from localized two-dimensional excitons in disordered quantum wells. Its spectral dependence and time dynamics are measured and theoretically predicted in a quantitative way. The intensity enhancement has a large momentum span extending beyond the external light emission cone. This is a consequence of the small localization length of the exciton as a massive particle probed close to the band bottom. The localization length can be controlled by the photon kinetic energy. This constitutes a qualitative difference to backscattering phenomena in other branches of physics.     

Localization properties of driven disordered one-dimensional systems

We generalize the definition of localization length to disordered systems driven by a time-periodic potential using a Floquet-Green function formalism. We study its dependence on the amplitude and frequency of the driving field in a one-dimensional tight-binding model with different amounts of disorder in the lattice. As compared to the autonomous system, the localization length for the driven system can increase or decrease depending on the frequency of the driving. We investigate the dependence of the localization length with the particle's energy and prove that it is always periodic. Its maximum is not necessarily at the band center as in the non-driven case. We study the adiabatic limit by introducing a phenomenological inelastic scattering rate which limits the delocalizing effect of low-frequency fields.     

Electronic localization at mesoscopic length scales: different definitions of localization and contact effects in a heuristic DNA model

In this work we investigate the electronic transport along model disordered DNA molecules using an effective tight-binding approach, addressing the localization properties. Different tools to investigate the degree of localization are examined as a function of system length, energy dependence and DNA to electrode coupling: localization length, participation number and sensitivity to boundary conditions. Combining the results obtained from these different tools, a thermodynamic limit for the model DNA molecule, within the mesoscopic length scale, can be established. Furthermore, three aspects are investigated: (i) the influence of strongly localized resonances on the localization length is discussed as an important mechanism defining the degree of localization for sizes below the thermodynamic limit; (ii) the dependence on the Hamiltonian parameters on a possible diffusive regime for short systems; and, finally, (iii) possible length dependent origins for the large discrepancies among experimental results for the electronic transport in DNA samples.     

Absence of quantum diffusion in a disordered elastic chain

A relation between localization of phonon modes in a disordered elastic chain and absence of quantum heat conductivity is shown. The frequency dependence of the localization length of normal modes is found at various degrees of disorder. The similarity of the problem of phonon localization and of electron localization is established.     

Routes towards Anderson-like localization of Bose-Einstein condensates in disordered optical lattices

We investigate, both experimentally and theoretically, possible routes towards Anderson-like localization of Bose-Einstein condensates in disordered potentials. The dependence of this quantum interference effect on the nonlinear interactions and the shape of the disorder potential is investigated. Experiments with an optical lattice and a superimposed disordered potential reveal the lack of Anderson localization. A theoretical analysis shows that this absence is due to the large length scale of the disorder potential as well as its screening by the nonlinear interactions. Further analysis shows that incommensurable superlattices should allow for the observation of the crossover from the nonlinear screening regime to the Anderson localized case within realistic experimental parameters.     

Interaction-assisted propagation of Coulomb-correlated electron-hole pairs in disordered semiconductors

A two-band model of a disordered semiconductor is used to analyze dynamical interaction induced weakening of localization in a system that is accessible to experimental verification. The results show a dependence on the sign of the two-particle interaction and on the optical excitation energy of the Coulomb-correlated electron-hole pair. Received 4 September and Received in final form 26 November 1998     

Coherence of elementary excitations in a disordered electron system

The localization properties of the single-particle and collective electron excitations were investigated in the intentionally disordered GaAs/AlGaAs superlattices by weak-field magnetoresistance and Raman scattering. The localization length of the individual electron was found to be considerably larger than that of the collective excitations. This suggests that the disorder has a weaker effect on the electrons than on their collective motion and that the interaction which gives rise to the collective effects increases localization.     

Interaction and localization effects in two-dimensional film of superconductor at T > Tc

The magnetic field and temperature dependence of the resistance of thin Al films have been investigated at T > T_c (T_c - superconducting transition temperature). The results are explained on the basis of localization and electron-electron interaction theory in two-dimensional disordered systems. The temperature dependence of inelastic scattering time and interaction constant for such films is found.     

Analytical study of the propagation of acoustic waves in a 1D weakly disordered lattice

This paper presents an analytical approach of the propagation of an acoustic wave through a normally distributed disordered lattice made up of Helmholtz resonators connected to a cylindrical duct. This approach allows to determine analytically the exact transmission coefficient of a weakly disordered lattice. Analytical results are compared to a well-known numerical method based on a matrix product. Furthermore, this approach gives an analytical expression of the localization length apart from the Bragg stopband which depends only on the standard deviation of the normal distribution disorder. This expression permits to study on one hand the localization length as a function of both disorder strength and frequency, and on the other hand, the propagation characteristics on the edges of two sorts of stopbands (Bragg and Helmholtz stopbands). Lastly, the value of the localization length inside the Helmholtz stopband is compared to the localization length in the Bragg stopband.     

Effect of disorder on magnetoresistance oscillations in nanoperforated superconducting TiN films

The low-temperature transport properties of nanoperforated superconducting TiN films have been experimentally studied. A periodic dependence of the resistance on an external magnetic field, with a period corresponding to a magnetic flux quantum per cell, is observed. An anomalous temperature dependence of the oscillation amplitude is found. The role of the effects of electron-electron interaction and localization in the physical properties of arrays of weak links, based on strongly disordered superconducting films, is discussed.     

Anomalous localization in low-dimensional systems with correlated disorder

This review presents a unified view on the problem of Anderson localization in one-dimensional weakly disordered systems with short-range and long-range statistical correlations in random potentials. The following models are analyzed: the models with continuous potentials, the tight-binding models of the Anderson type, and various Kronig–Penney models with different types of perturbations. Main attention is paid to the methods of obtaining the localization length in dependence on the controlling parameters of the models. Specific interest is in an emergence of effective mobility edges due to certain long-range correlations in a disorder. The predictions of the theoretical and numerical analysis are compared to recent experiments on microwave transmission through randomly filled waveguides.     

Interaction induced delocalization of two particles: large system size calculations and dependence on interaction strength

The localization length L₂ of two interacting particles in a one-dimensional disordered system is studied for very large system sizes by an efficient and accurate variant of the Green function method. The numerical results (at the band center) can be well described by the functional form L ₂ =L ₁ [0.5+c(U) L ₁ ] where L₁ is the one-particle localization length and the coefficient depends on the strength U of the on-site Hubbard interaction. The Breit-Wigner width or equivalently the (inverse) life time of non-interacting pair states is analytically calculated for small disorder and taking into account the energy dependence of the one-particle localization length. This provides a consistent theoretical explanation of the numerically found U-dependence of c(U). Received 16 September 1998     

Decay of high-frequency acoustic excitations in chain-type lattices and weak localization

The attenuation of high-frequency sound in disordered quasi-one-dimensional semiconducting and dielectric crystals, which is associated with three-phonon decay and elastic scattering by structure defects is considered theoretically. It is shown that specific interference processes occurring in the regime of weak localization of acoustic vibrational excitations considerably affect the propagation of sound. This mechanism of sound attenuation can be observed experimentally from the anomalies in the frequency dependence of the reciprocal attenuation length of sound.     

Suppression of Anderson localization in disordered metamaterials

We study wave propagation in mixed, 1D disordered stacks of alternating right- and left-handed layers and reveal that the introduction of metamaterials substantially suppresses Anderson localization. At long wavelengths, the localization length in mixed stacks is orders of magnitude larger than for normal structures, proportional to the sixth power of the wavelength, in contrast to the usual quadratic wavelength dependence of normal systems. Suppression of localization is also exemplified in long-wavelength resonances which largely disappear when left-handed materials are introduced.     

Frequency-dependent localization length of SH-wave in randomly disordered piezoelectric phononic crystals

In this paper, the localization length that represents the distance of elastic waves propagating along the disordered periodic structures is defined as the reciprocal of the smallest positive Lyapunov exponent, i.e. the localization factor. The algorithm for determining all the Lyapunov exponents in continuous dynamic systems presented by Wolf et al. is employed to calculate those in discrete dynamic systems. Numerical results of the localization lengths of SH-wave are presented and discussed in ordered and disordered piezoelectric phononic crystals to identify the different effect degrees for the decay of electrical potential in the polymers and the randomness on the localization level. For the disordered case, disorder in the thickness of the polymers and disorder in the elastic constant of the piezoelectric ceramics are all considered. The results show that some parameters such as the incident angle of elastic wave, the randomness degree and the piezoelectricity of piezoelectric ceramics and so on have pronounced effects on the frequency-dependent localization length.     

Mobility edge in the three dimensional Anderson model

The localization length as a function of energy and disorder of a three dimensional disordered system described by the Anderson Hamiltonian is determined. The phase diagram for localization is discussed with particular emphasis on the mechanisms which are important for localization (quantum interference and tunneling).     

Electronic transport through superlattice-like disordered carbon nanotubes

We introduce a simple method for investigating electronic transport in pure and superlattice-like disordered carbon nanotubes (SDCNTs). This model reduces the numerical calculation time and enables us to use the transfer matrix method to investigate transport in a carbon nanotube (CNT). Therefore, we consider an SDCNT device attached to metallic CNT leads, taking into account the disorder effect. Our calculations are based on the tight-binding model and the transfer matrix method. We concentrate on the localization length and density of sates (DOS) for various strengths of disorder. Our numerical results show a nearly steplike dependence of the localization length on energy at small disorder concentration. By controlling the disorder concentration and wire length, this kind of system can explain the extended states from the localized states. Our results can serve as a base for developments in designing nano-electronic devices.     

Wave localization in randomly disordered multi-coupled multi-span beams on elastic foundations

In this paper, the wave propagation and localization in randomly disordered periodic multi-span beams on elastic foundations are studied. For two kinds of beams, i.e. the multi-span beams on elastic foundations with periodic flexible and simple supports, the transfer matrices between two consecutive sub-spans are obtained by means of the continuity conditions. The algorithm for determining all the Lyapunov exponents in continuous dynamic systems presented by Wolf et al. is employed to calculate those in discrete dynamic systems. The localization factor characterizing the average exponential rates of growth or decay of wave amplitudes along the disordered beams is defined as the smallest positive Lyapunov exponent of the discrete dynamical system. The localization length that represents the distance of elastic waves propagating along the disordered periodic structures is defined as the reciprocal of the smallest positive Lyapunov exponent, i.e. the localization factor. For the two kinds of disordered periodic beams on elastic foundations, the numerical results of the localization factors are presented and analysed by comparing them with the results of the beams without elastic foundations to illustrate the effects of the elastic foundations on the wave propagation and localization. The effects of the disorder of span-length and the dimensionless torsional and linear spring stiffness on the localization factors are discussed. Moreover, the localization lengths are also calculated and discussed for certain structural parameters in disordered periodic structures. It can be observed from the results that ordered periodic multi-span beams have the characteristics of the frequency passbands and stopbands and the localization of elastic waves can occur in disordered periodic systems: the localization degree of elastic waves is strengthened with the increase of the coefficient of variation of the span-length. The influences of the elastic foundations on the wave propagation and localization are more complicated. Generally speaking, in lower-frequency regions the elastic foundations have pronounced effects on the spectral structures, but in higher-frequency regions the effects are negligible. The localization degree increases as the torsional spring stiffness increases. The linear spring has few effects on the spectral structures in higher-frequency regions, but in lower-frequency regions it has prominent effects. The larger the disorder degree, the shorter the non-dimensional localization length.