Yu. V. Tarasov

Conductance of a single-mode electron waveguide with statistically identical rough boundaries

The transport characteristics of pure narrow 2D conductors, in which the electron scattering is caused by rough side boundaries, have been studied. The conductance of such strips is highly sensitive to the intercorrelation properties of inhomogeneities of the opposite edges. The case with completely correlated statistically identical boundaries (CCB) is a peculiar one. Herein the electron scattering is uniquely due to fluctuations of the asperity slope and is not related to the strip width fluctuations. Owing to this, the electron relaxation lengths, and specifically the localization length, depend quite differently on the asperity parameters as compared to the case for conductors with arbitrarily intercorrelated edges. A method for calculating the dynamical characteristics of the CCB electron waveguides is proposed clear of any restrictions on the asperity height.

Elastic scattering as a cause of quantum dephasing: the conductance of two-dimensional imperfect conductors

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.

Spectral properties of cylindrical quasioptical cavity resonator with random inhomogeneous side boundary.

A rigorous solution for the spectrum of a quasioptical cylindrical cavity resonator with a randomly rough side boundary has been obtained. To accomplish this task, we have developed a method for the separation of variables in a wave equation, which enables one, in principle, to rigorously examine any limiting case — from negligibly weak to arbitrarily strong disorder at the resonator boundary. It is shown that the effect of disorder-induced scattering can be properly described in terms of two geometric potentials, specifically, the “amplitude” and the “gradient” potentials, which appear in wave equations in the course of conformal smoothing of the resonator boundaries. The scattering resulting from the gradient potential appears to be dominant, and its impact on the whole spectrum is governed by the unique sharpness parameter Ξ, the mean tangent of the asperity slope. As opposed to the resonator with bulk disorder, the distribution of nearest-neighbor spacings (NNS) in the rough-resonator spectrum acquires Wigner-like features only when the governing wave operator loses its unitarity, i. e., with the availability in the system of either openness or dissipation channels. It is shown that the reason for this is that the spectral line broadening related to the oscillatory mode scattering due to random inhomogeneities is proportional to the dissipation rate. Our numeric experiments suggest that in the absence of dissipation loss the randomly rough resonator spectrum is always regular, whatever the degree of roughness. Yet, the spectrum structure is quite different in the domains of small and large values of the parameter Ξ. For the dissipation-free resonator, the NNS distribution changes its form with growing the asperity sharpness from Poissonian-like distribution in the limit of Ξ ≪ 1 to the bell-shaped distribution in the domain where Ξ ≫ 1.

Effect of random surface inhomogeneities on spectral properties of dielectric-disk microresonators: theory and modeling at millimeter wave range.

The influence of random axially homogeneous surface roughness on spectral properties of dielectric resonators of circular disk form is studied both theoretically and experimentally. To solve the equations governing the dynamics of electromagnetic fields, the method of eigenmode separation is applied previously developed with reference to inhomogeneous systems subject to arbitrary external static potential. We prove theoretically that it is the gradient mechanism of wave-surface scattering that is highly responsible for nondissipative loss in the resonator. The influence of side-boundary inhomogeneities on the resonator spectrum is shown to be described in terms of effective renormalization of mode wave numbers jointly with azimuth indices in the characteristic equation. To study experimentally the effect of inhomogeneities on the resonator spectrum, the method of modeling in the millimeter wave range is applied. As a model object, we use a dielectric disk resonator (DDR) fitted with external inhomogeneities randomly arranged at its side boundary. Experimental results show good agreement with theoretical predictions as regards the predominance of the gradient scattering mechanism. It is shown theoretically and confirmed in the experiment that TM oscillations in the DDR are less affected by surface inhomogeneities than TE oscillations with the same azimuth indices. The DDR model chosen for our study as well as characteristic equations obtained thereupon enable one to calculate both the eigenfrequencies and the Q factors of resonance spectral lines to fairly good accuracy. The results of calculations agree well with obtained experimental data.

Propagation of wave packets in randomly stratified media.

The propagation of a narrow-band signal radiated by a point source in a randomly layered absorbing medium is studied asymptotically in the weak-scattering limit. It is shown that in a disordered stratified medium that is homogeneous on average, a pulse is channelled along the layers in a narrow strip in the vicinity of the source. The space-time distribution of the pulse energy is calculated. Far from the source, the shape of wave packets is universal and independent of the frequency spectrum of the radiated signal. Strong localization effects manifest themselves also as a low-decaying tail of the pulse and a strong time delay in the direction of stratification. The frequency-momentum correlation function in a one-dimensional random medium is calculated.

Plasmon-polaritons on a surface with fluctuating impedance: Scattering, localization, stability

Scattering of TM-polarized surface plasmon-polariton waves (PPW) by a finite segment of the metal–vacuum interface with randomly fluctuating surface impedance is examined. Solution of the integral equation relating the scattered field with the field of the incident PPW, valid for arbitrary scattering intensity and arbitrary dissipative characteristics of the conductive medium, is analyzed. As a measure of the PPW scattering, the Hilbert norm of the integral scattering operator is used. The strength of the scattering is shown to be determined not only by the parameters of the fluctuating impedance (dispersion, correlation radius and the length of the inhomogeneity region) but also by the conductivity of the metal. If the scattering operator norm is small, the PPW is mainly scattered into the vacuum, thus losing its energy through the excitation of quasi-isotropic bulk Norton waves above the conducting surface. The scattered field intensity is expressed in terms of the random impedance pair-correlation func...

Spectrum of an open disordered quasi-two-dimensional electron system : The mode reduction effect of a classically weak in-plane magnetic field

The effect of an in-plane magnetic field upon open quasi-two-dimensional electron and hole systems is investigated in terms of the carrier ground-state spectrum. The magnetic field, classified as weak from the viewpoint of correlation between size parameters of classical electron motion and the gate potential spatial profile is shown to efficiently cutoff extended modes from the spectrum and to change singularly the mode density of states (MDOS). The reduction in the number of current-carrying modes, right up to zero in magnetic fields of moderate strength, can be viewed as the cause of magnetic-field-driven metal-to-insulator transition widely observed in two-dimensional systems. Both the mode number reduction and the MDOS singularity appear to be most pronounced in the mode states dephasing associated with their scattering by quenched-disorder potential. This sort of dephasing is proven to dominate the dephasing which involves solely the magnetic field whatever level of the disorder.

Single-particle scenario of the metal–insulator transition in two-dimensional systems at T=0

The conductance of disordered electron systems of finite size is calculated by reducing the initial dynamical problem of arbitrary dimensionality to strictly one-dimensional problems for single-particle mode propagators. It is shown that the metallic ground state of two-dimensional conductors, considered as a limiting case of three-dimensional quantum waveguides, is due to their multimode nature. As the thickness of the waveguide is decreased, e.g., with the aid of a “pressing” potential, the electron system undergoes a sequence of continuous quantum phase transitions involving a discrete change in the number of extended modes. The closing of the last current-carrying mode is interpreted as a phase transition of the electron system from the metallic to an insulator state. The results agree qualitatively with the observed “anomalies” of the resistance of various two-dimensional electron and hole systems.

Conductance of two-dimensional imperfect conductors: does the elastic scattering preclude localization at T = 0?

Elastic electron-impurity scattering is proven analytically to prevent interferential localization in two-dimensional wires with more than one conducting channel. An unconventional diffusive regime is found in the length region where the electrons are usually considered as localized. An ohmic, rather than exponential, dependence of the T = 0 conductance is predicted, with a length-dependent diffusion coefficient.

One-particle conductance of an open quasi-two-dimensional Fermi system: Evidence of the parallel-magnetic-field-induced mode reduction effect

The conductance of an open quench-disordered two-dimensional (2D) electron system subject to an in-plane magnetic field is calculated within the framework of conventional Fermi liquid theory applied to actually a three-dimensional system of spinless electrons confined to a highly anisotropic (planar) near-surface potential well. Using the calculation method suggested in this paper, the magnetic field piercing a finite range of infinitely long system of carriers is treated as introducing the additional highly non-local scatterer which separates the circuit thus modelled into three parts -- the system as such and two perfect leads. The transverse quantization spectrum of the inner part of the electron waveguide thus constructed can be effectively tuned by means of the magnetic field, even though the least transverse dimension of the waveguide is small compared to the magnetic length. The initially finite (metallic) value of the conductance, which is attributed to the existence of extended modes of the transverse quantization, decreases rapidly as the magnetic field grows. This decrease is due to the mode number reduction effect produced by the magnetic field. The closing of the last current-carrying mode, which is slightly sensitive to the disorder level, is suggested as the origin of the magnetic-field-driven metal-to-insulator transition widely observed in 2D systems.