V. Freilikher

Electronic properties of mesoscopic graphene structures: Charge confinement and control of spin and charge transport

This brief review discusses electronic properties of mesoscopic graphene-based structures. These allow controlling the confinement and transport of charge and spin; thus, they are of interest not only for fundamental research, but also for applications. The graphene-related topics covered here are: edges, nanoribbons, quantum dots, pn-junctions, pnp-structures, and quantum barriers and waveguides. This review is partly intended as a short introduction to graphene mesoscopics.

Optical dislocation networks in highly random media

Abstract Networks of optical dislocations in gaussian speckle patterns are studied both theoretically and experimentally. A simple product wavefunction is suggested to describe an arbitrary dislocation network. Phase maps predicted by this wavefunction are tested against measured interferograms for a variety of different dislocations and good agreement is found between theory and experiment. Simple arguments based upon the sampling theorem are presented which suggest that in the gaussian limit the dislocation network contains all the information needed to reconstruct the total wavefield, and alternatively, that the wavefield may also be reconstructed from a small fragment of the phase map using the method of zero crossings. It is also argued that there must exist some degree of correlation between neighboring dislocations.

Colloquium: Unusual resonators: Plasmonics, metamaterials, and random media

Superresolution, extraordinary transmission, total absorption, and localization of electromagnetic waves are currently attracting growing attention. These phenomena are related to different physical objects and are usually studied within the context of different, sometimes rather sophisticated, physical approaches. Remarkably, all these seemingly unrelated phenomena owe their origin to the same underlying physical mechanism - wave interaction with an open resonator. Here we show that it is possible to describe all of these effects in a unified way, mapping each system onto a simple resonator model. Such description provides a thorough understanding of the phenomena, explains all the main features of their complex behaviour, and enables to control the system via the resonator parameters: eigenfrequencies, Q-factors, and coupling coefficients.

Transport and localization in periodic and disordered graphene superlattices

We study the transport of low-energy charged quasiparticles in graphene superlattices created by applying either periodic or disordered smooth scalar potentials, which cause no intervalley scattering. It is shown that the transport and spectral properties of such structures are strongly anisotropic. In the direction perpendicular to the layers, the eigenstates in a disordered sample are delocalized for all energies and provide a minimum nonzero conductivity, which cannot be destroyed by disorder, no matter how strong this is. However, along with extended states, there exist discrete sets of angles and energies with exponentially localized eigenfunctions (disorder-induced resonances). Owing to these features, such samples could be used as building blocks in tunable electronic circuits. It is shown that, depending on the type of the unperturbed system, the disorder could either suppress or enhance the transmission. Remarkable properties of the transmission have been found in graphene systems built of alternating

Coherent scattering enhancement in systems bounded by rough surfaces

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Bistability of Anderson localized states in nonlinear random media

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Reflection and transmission of waves in surface-disordered waveguides

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Soil moisture (water-content) assessment by an airborne scatterometer: the Chernobyl disaster area and the Negev desert.

junctions. The mean transmission coefficient has anomalously narrow angular spectrum, practically independent of the amplitude of the fluctuations of the potential. To better understand the physical implications of the results presented here, most of these have been compared with the results for analogous electromagnetic wave systems. Along with similarities, a number of quite surprising differences have been found.

Localized Modes in Open One-Dimensional Dissipative Random Systems

Abstract When an electromagnetic wave is incident on a bounded random system that supports two or more discrete eigenmodes at the frequency of the incident wave, the angular distribution of the intensity of the fields scattered incoherently from, and transmitted incoherently through, the system can display peaks at special scattering angles and angles of transmission, determined by degenerate time-reversal symmetry, in addition to the well-known enhanced backscattering and enhanced transmission peaks. These additional peaks are multiple-scattering phenomena caused by the coherent interference between each multiply-scattered wave and a degenerate time-reversed partner. We illustrate both analytically and numerically the occurrence of satellite peaks in scattering and transmission in the case that the scattering system is a thin, supported, dielectric film, and in the case that it is a free-standing metal film, into which the randomness is introduced by making the illuminated surface of each film a one-dimensional, random surface. The origins of the satellite peaks, and their positions are explained on the basis of a simple argument based on the phase coherence of multiply-scattered trajectories mediated by the degenerate surface or guided waves supported by each of these structures. Perturbative and computational approaches to the calculation of the scattering and transmission spectra are described, and experimental conditions most favorable for the observation of the predicted features are presented. The coherent interference of multiply-scattered fields affects drastically the time evolution of a wave packet (electron or electromagnetic pulse) injected into a closed disordered cavity. We show that in this case conventional perturbative methods are inapplicable for the calculation of the statistical moments of the wave field, and introduce the random matrix theory (RMT) approach for the description of disordered closed systems. The statistics of the eigenlevels and eigenfunctions of such systems is studied employing the RMT method for different types of symmetry. The existence of coherent enhancement (a peak in the stationary distribution of the intensity of a pulse) in cavities with random boundaries is demonstrated analytically, and confirmed by numerical experiments in an acoustic resonator with random boundaries.

Enhanced transmission due to disorder.

We study wave transmission through one-dimensional random nonlinear structures and predict a novel effect resulting from an interplay of nonlinearity and disorder. We reveal that, while weak nonlinearity does not change the typical exponentially small transmission in the regime of the Anderson localization, it affects dramatically the disorder-induced localized states excited inside the medium leading to bistable and nonreciprocal resonant transmission. Our numerical modeling shows an excellent agreement with theoretical predictions based on the concept of a high-Q resonator associated with each localized state. This offers a new way for all-optical light control employing statistically homogeneous random media without regular cavities.