Statistical properties of wave transport through surface-disordered waveguides

We review some general statistical properties of wave transport through surface disordered waveguides. These systems are shown to present both striking similarities and differences with respect to quasi-one-dimensional waveguides with volume disorder. The statistical properties are analysed using extensive numerical calculations and random matrix theory results. The transport properties are characterized by the statistical behaviour of different transport coefficients that can be defined for both classical (light, microwaves, sound, etc.) and quantum (electrons) waves. In analogy with bulk-disordered systems, the behaviour of the waveguide conductance/resistance (defined for both classical and quantum waves) as a function of the system length defines three different transport regimes: ballistic, diffusive and localization. However, the coupling between waveguide modes presents significant differences with respect to the coupling induced by volume defects. For any incoming mode, there is a strong preference for the forward propagation through the lowest mode. For narrow waveguides, the statistics of reflection coefficients (reflected speckle pattern) present strong finite-size effects which can be surprisingly well described by random matrix theory. Special attention is paid to the fundamental problem of the transition between different regimes. The long-standing problems of the phase randomization process between ballistic and diffusive regimes and the evolution of the conductance statistical distribution in the transition from diffusion (Gaussian statistics) to localization (log normal statistics) are also discussed.     

Quantum thermal transport from classical molecular dynamics

Using a generalized Langevin equation of motion, quantum thermal transport is obtained from classical molecular dynamics. This is possible because the heat baths are represented by random noises obeying quantum Bose-Einstein statistics. The numerical method gives asymptotically exact results in both the low-temperature ballistic transport regime and the high-temperature strongly nonlinear classical regime. The method is a quasiclassical approximation to the quantum transport problem. A one-dimensional quartic on-site model is used to demonstrate the crossover from ballistic to diffusive thermal transport.     

Role of orbital dynamics in spin relaxation and weak antilocalization in quantum dots

We develop a semiclassical theory for spin-dependent quantum transport to describe weak (anti)localization in quantum dots with spin-orbit coupling. This allows us to distinguish different types of spin relaxation in systems with chaotic, regular, and diffusive orbital classical dynamics. We find, in particular, that for typical Rashba spin-orbit coupling strengths, integrable ballistic systems can exhibit weak localization, while corresponding chaotic systems show weak antilocalization. We further calculate the magnetoconductance and analyze how the weak antilocalization is suppressed with decreasing quantum dot size and increasing additional in-plane magnetic field.     

Unified semiclassical approach to electronic transport from diffusive to ballistic regimes

We show that by integrating out the electric field and incorporating proper boundary conditions,a Boltzmann equation can describe electron transport properties,continuously from the diffusive to ballistic regimes.General analytical formulas of the conductance in D = 1,2,3 dimensions are obtained,which recover the Boltzmann–Drude formula and Landauer–B ¨uttiker formula in the diffusive and ballistic limits,respectively.This intuitive and efficient approach can be applied to investigate the interplay of system size and impurity scattering in various charge and spin transport phenomena,when the quantum interference effect is not important.     

Charge transport in carbon nanotubes based materials: a Kubo–Greenwood computational approach

In this contribution, we present a numerical study of quantum transport in carbon nanotubes based materials. After a brief presentation of the computational approach used to investigate the transport coefficient (Kubo method), the scaling properties of quantum conductance in ballistic regime as well as in the diffusive regimes are illustrated. The impact of elastic (impurities) and dynamical disorders (phonon vibrations) are analyzed separately, with the extraction of main transport length scales (mean free path and localization length), as well as the temperature dependence of the nanotube resistance. The results are found in very good agreement with both analytical results and experimental data, demonstrating the predictability efficiency of our computational strategy. To cite this article: H. Ishii et al., C. R. Physique 10 (2009).     

Quantum interference electronic switch

A novel planar electron waveguide coupler is proposed as an electronic switch. The structure consists of two quantum wires interconnected by a dual branch coupling scheme which is assumed to be controlled by an electrostatic potential. Switching is provided by tuning the phase relations between the different scattered waves by the two coupling branch lines. Assuming ballistic transport, the analysis is conducted by solving the time independent two-dimensional Schrödinger equation in order to derive the conductance characteristics. At a resonant energy of 25 meV and for a waveguide width of 27.4 nm, over 90% of the electron wave has been transferred with a half picosecond time response.     

Weak localization in mesoscopic hole transport: berry phases and classical correlations

We consider phase-coherent transport through ballistic and diffusive two-dimensional hole systems based on the Kohn-Luttinger Hamiltonian. We show that intrinsic heavy-hole-light-hole coupling gives rise to clear-cut signatures of an associated Berry phase in the weak localization which renders the magnetoconductance profile distinctly different from electron transport. Nonuniversal classical correlations determine the strength of these Berry phase effects and the effective symmetry class, leading even to antilocalization-type features for circular quantum dots and Aharonov-Bohm rings in the absence of additional spin-orbit interaction. Our semiclassical predictions are confirmed by numerical calculations.     

Diffusive transport in highly corrugated channels

Diffusion in waveguides with spatially modulated profiles is an important topic in modern electromagnetics and optics. Wave dynamics in the high-frequency asymptotics are governed by classical ray dynamics which can be characterised by looking at the diffusion of particles throughout the channel. We study the transport of particles (rays) in a channel with a sinusoidal profile at different values of the corrugation amplitude. We find that below a certain corrugation level the transport is ballistic, beyond this threshold, a diffusion-like behaviour emerges in the asymptotic limit of large times. In this regime particle transport slows down due to the trapping mechanism in the corrugated regions of the channel. We use the analogy with correlated random walks to discuss the observed transport regimes.     

Editorial

Abstract

A method is proposed for studying wave and particle transport in disordered waveguide systems of dimension higher than unity by means of exact one-dimensionalization of the dynamic equations in the mode representation. As a particular case, the T=0 conductance of a two-dimensional quantum wire is calculated, which exhibits ohmic behaviour, with length-dependent conductivity, at any conductor length exceeding the electron quasi-classical mean free path. The unconventional diffusive regime of charge transport is found in the range of conductor lengths where the electrons are commonly considered as localized. In quantum wires with more than one conducting channel, each being identified with the extended waveguide mode, the inter-mode scattering is proven to serve as a phase-breaking mechanism that prevents interference localization without real inelasticity of interaction.     

Statistics of waves propagating in a random medium

We present a review of part of the results obtained by the authors for the statistics of coherent radiation propagating in a random medium both in the framework of diagrammatic techniques and random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission coefficient for the diffusive transport and the crossover between the diffusive and ballistic regimes are obtained.The authors acknowledge the financial support of the Israeli Academy of Sciences and of the Schottenstein Center.     

Quantum interference and ballistic transmission in nanotube electron waveguides

The electron transport properties of well-contacted individual single-walled carbon nanotubes are investigated in the ballistic regime. Phase coherent transport and electron interference manifest as conductance fluctuations as a function of Fermi energy. Resonance with standing waves in finite-length tubes and localized states due to imperfections are observed for various Fermi energies. Two units of quantum conductance 2G(0) = 4e(2)/h are measured for the first time, corresponding to the maximum conductance limit for ballistic transport in two channels of a nanotube.     

Universal spin-Hall conductance fluctuations in two dimensions

We report a theoretical investigation on spin-Hall conductance fluctuation of disordered four-terminal devices in the presence of Rashba or/and Dresselhaus spin-orbital interactions in two dimensions. As a function of disorder, the spin-Hall conductance GsH shows ballistic, diffusive, and insulating transport regimes. For given spin-orbit interactions, a universal spin-Hall conductance fluctuation (USCF) is found in the diffusive regime. The value of the USCF depends on the spin-orbit coupling tso but is independent of other system parameters. It is also independent of whether Rashba or Dresselhaus or both spin-orbital interactions are present. When tso is comparable to the hopping energy t, the USCF is a universal number approximately 0.18e/4pi. The distribution of GsH crosses over from a Gaussian distribution in the metallic regime to a non-Gaussian distribution in the insulating regime as the disorder strength is increased.     

Quantum coherent effects in Anderson insulators

During the last two decades quantum interference effects have been extensively studied in the transport properties of diffusive systems such as metals and semiconductors. When the spatial disorder in these systems exceeds a critical value the electronic wavefunctions are localized and their ground state is insulating (the Anderson transition). At finite temperatures charge transport in this phase involves phonon-assisted tunnelling between localized states. This mode of transport is purely quantum mechanical and has no classical analogue. Anderson insulators are therefore the paradigmatic system for studying interference phenomena of electron waves in random media. In this paper we discuss the question of quantum coherence in Anderson insulators and review some of the experimental manifestations of interference phenomena in their transport properties.     

Ehrenfest-time dependence of weak localization in open quantum dots

Semiclassical theory predicts that the weak localization correction to the conductance of a ballistic chaotic cavity is suppressed if the Ehrenfest time exceeds the dwell time in the cavity [I. L. Aleiner and A. I. Larkin, Phys. Rev. B 54, 14423 (1996)]. We report numerical simulations of weak localization in the open quantum kicked rotator that confirm this prediction. Our results disagree with the "effective random matrix theory" of transport through ballistic chaotic cavities.     

Ballistic Quantum Transport: Effect of Geometrical Phases

We study the influence of nonuniform magnetic fields on the magneto conductance of mesoscopic microstructures. We show that the coupling of the electron spin to the inhomogenous field gives rise to effects of the Berry phase on ballistic quantum transport and discuss adiabaticity conditions required to observe such effects. We present numerical results for different ring geometries showing a splitting of Aharonov–Bohm conductance peaks for single rings and corresponding signatures of the geometrical phase in weak localization. The latter features can be qualitatively explained in a semiclassical approach to quantum transport.     

Transmission eigenvalues and the bare conductance in the crossover to Anderson localization

We measure the field transmission matrix t for microwave radiation propagating through random waveguides in the crossover to Anderson localization. From these measurements, we determine the dimensionless conductance g and the individual eigenvalues τ(n) of the transmission matrix tt(?) whose sum equals g. In diffusive samples, the highest eigenvalue, τ(1), is close to unity corresponding to a transmission of nearly 100%, while for localized waves, the average of τ(1), is nearly equal to g. We find that the spacing between average values of lnτ(n) is constant and demonstrate that when surface interactions are taken into account it is equal to the inverse of the bare conductance.     

初态对光波导阵列中连续量子行走影响的研究

本文使用近邻耦合模型得到的解析解,分析了周期性波导中输入态对量子行走的粒子数的概率分布函数 和二阶相干性的影响.结果表明:输入态的对称性质对量子行走过程的二阶相干度有影响, 而对粒子数的概率分布函数影响不大. 关键词： 周期性光波导阵列 量子行走 二阶相干度 纠缠态     

Anderson localization and nonlinearity in one-dimensional disordered photonic lattices

We experimentally investigate the evolution of linear and nonlinear waves in a realization of the Anderson model using disordered one-dimensional waveguide lattices. Two types of localized eigenmodes, flat-phased and staggered, are directly measured. Nonlinear perturbations enhance localization in one type and induce delocalization in the other. In a complementary approach, we study the evolution on short time scales of delta-like wave packets in the presence of disorder. A transition from ballistic wave packet expansion to exponential (Anderson) localization is observed. We also find an intermediate regime in which the ballistic and localized components coexist while diffusive dynamics is absent. Evidence is found for a faster transition into localization under nonlinear conditions.     

Decoherence and disorder in quantum walks: from ballistic spread to localization

We investigate the impact of decoherence and static disorder on the dynamics of quantum particles moving in a periodic lattice. Our experiment relies on the photonic implementation of a one-dimensional quantum walk. The pure quantum evolution is characterized by a ballistic spread of a photon's wave packet along 28 steps. By applying controlled time-dependent operations we simulate three different environmental influences on the system, resulting in a fast ballistic spread, a diffusive classical walk, and the first Anderson localization in a discrete quantum walk architecture.     

Dual nature of localization in guiding systems with randomly corrugated boundaries: Anderson-type versus entropic

A unified theory for the conductance of an infinitely long multimode quantum wire whose finite segment has randomly rough lateral boundaries is developed. It enables one to rigorously take account of all feasible mechanisms of wave scattering, both related to boundary roughness and to contacts between the wire rough section and the perfect leads within the same technical frameworks. The rough part of the conducting wire is shown to act as a mode-specific randomly modulated effective potential barrier whose height is governed essentially by the asperity slope. The mean height of the barrier, which is proportional to the average slope squared, specifies the number of conducting channels. Under relatively small asperity amplitude this number can take on arbitrary small, up to zero, values if the asperities are sufficiently sharp. The consecutive channel cut-off that arises when the asperity sharpness increases can be regarded as a kind of localization, which is not related to the disorder per se but rather is of entropic or (equivalently) geometric origin. The fluctuating part of the effective barrier results in two fundamentally different types of guided wave scattering, viz., inter- and intramode scattering. The intermode scattering is shown to be for the most part very strong except in the cases of (a) extremely smooth asperities, (b) excessively small length of the corrugated segment, and (c) the asperities sharp enough for only one conducting channel to remain in the wire. Under strong intermode scattering, a new set of conducting channels develops in the corrugated waveguide, which have the form of asymptotically decoupled extended modes subject to individual solely intramode random potentials. In view of this fact, two transport regimes only are realizable in randomly corrugated multimode waveguides, specifically, the ballistic and the localized regime, the latter characteristic of one-dimensional random systems. Two kinds of localization are thus shown to coexist in waveguide-like systems with randomly corrugated boundaries, specifically, the entropic localization and the one-dimensional Anderson (disorder-driven) localization. If the particular mode propagates across the rough segment ballistically, the Fabry–Pérot-type oscillations should be observed in the conductance, which are suppressed for the mode transferred in the Anderson-localized regime.