Physico-Technical Institute

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of large sizes of these networks, the distances between most their vertices are short — a feature known as the “smallworld” effect. We discuss how growing networks self-organize into scale-free structures and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in Nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems

The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years, important steps have been made toward understanding the qualitatively new critical phenomena in complex networks. The results, concepts, and methods of this rapidly developing field are reviewed. Two closely related classes of these critical phenomena are considered, namely, structural phase transitions in the network architectures and transitions in cooperative models on networks as substrates. Systems where a network and interacting agents on it influence each other are also discussed. A wide range of critical phenomena in equilibrium and growing networks including the birth of the giant connected component, percolation, $k$-core percolation, phenomena near epidemic thresholds, condensation transitions, critical phenomena in spin models placed on networks, synchronization, and self-organized criticality effects in interacting systems on networks are mentioned. Strong finite-size effects in these systems and open problems and perspectives are also discussed.

Abstract The optical properties of excitonic recombinations in bulk, n‐type ZnO are investigated by photoluminescence (PL) and spatially resolved cathodoluminescence (CL) measurements. At liquid helium temperature in undoped crystals the neutral donor bound excitons dominate in the PL spectrum. Two electron satellite transitions (TES) of the donor bound excitons allow to determine the donor binding energies ranging from 46 to 73 meV. These results are in line with the temperature dependent Hall effect measurements. In the as‐grown crystals a shallow donor with an activation energy of 30 meV controls the conductivity. Annealing annihilates this shallow donor which has a bound exciton recombination at 3.3628 eV. Correlated by magnetic resonance experiments we attribute this particular donor to hydrogen. The Al, Ga and In donor bound exciton recombinations are identified based on doping and diffusion experiments and using secondary ion mass spectroscopy. We give a special focus on the recombination around 3.333 eV, i.e. about 50 meV below the free exciton transition. From temperature dependent measurements one obtains a small thermal activation energy for the quenching of the luminescence of 10 ± 2 meV despite the large localization energy of 50 meV. Spatially resolved CL measurements show that the 3.333 eV lines are particularly strong at crystal irregularities and occur only at certain spots hence are not homogeneously distributed within the crystal contrary to the bound exciton recombinations. We attribute them to excitons bound to structural defects (Y‐line defect) very common in II–VI semiconductors. For the bound exciton lines which seem to be correlated with Li and Na doping we offer a different interpretation. Li and Na do not introduce any shallow acceptor level in ZnO which otherwise should show up in donor–acceptor pair recombinations. Nitrogen creates a shallow acceptor level in ZnO. Donor–acceptor pair recombination with the 165 meV deep N‐acceptor is found in nitrogen doped and implanted ZnO samples, respectively. In the best undoped samples excited rotational states of the donor bound excitons can be seen in low temperature PL measurements. At higher temperatures we also see the appearance of the excitons bound to the B‐valence band, which are approximately 4.7 meV higher in energy. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A phenomenological thermodynamic theory of ferroelectric thin films epitaxially grown on cubic substrates is developed using a new form of the thermodynamic potential, which corresponds to the actual mechanical boundary conditions of the problem. For single-domain ${\mathrm{BaTiO}}_{3}$ and ${\mathrm{PbTiO}}_{3}$ films, the ``misfit-temperature'' phase diagrams are constructed. It is found that the 2D clamping of the films, apart from a shift of the temperature of the ferroelectric transition, results in a change of its order. A change of the sequence of the phases and the appearance of phases forbidden in the bulk crystals are predicted.

The model of growing networks with the preferential attachment of new links is generalized to include initial attractiveness of sites. We find the exact form of the stationary distribution of the number of incoming links of sites in the limit of long times, $P(q)$, and the long-time limit of the average connectivity $\overline{q}(s,t)$ of a site $s$ at time $t$ (one site is added per unit of time). At long times, $P(q)\ensuremath{\sim}{q}^{\ensuremath{-}\ensuremath{\gamma}}$ at $q\ensuremath{\rightarrow}\ensuremath{\infty}$ and $\overline{q}(s,t)\ensuremath{\sim}(s/t{)}^{\ensuremath{-}\ensuremath{\beta}}$ at $s/t\ensuremath{\rightarrow}0$, where the exponent $\ensuremath{\gamma}$ varies from $2$ to $\ensuremath{\infty}$ depending on the initial attractiveness of sites. We show that the relation $\ensuremath{\beta}(\ensuremath{\gamma}\ensuremath{-}1)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ between the exponents is universal.

We demonstrate that electrons in a ballistic field effect transistor behave as a fluid similar to shallow water. Phenomena similar to wave and soliton propagation, hydraulic jump, and others should take place in this electron fluid. We show that a relatively slow electron flow should be unstable because of plasma wave amplification due to the reflection from the device boundaries. This provides a new mechanism for the generation of tunable far infrared electromagnetic radiation.

Prethermalization When a physical system is subjected to a rapid change of conditions (for example, a gas of atoms is allowed to occupy a volume twice the size of the original container), it quickly achieves a new temperature (thermalizes) through collisions. However, in some quantum systems many conserved variables inhibit thermalization; understanding the phases the systems go through in the slowing process is of great interest to cosmologists and physicists. Gring et al. (p. 1318 , published online 31 August) separate an ultracold one-dimensional gas of bosonic atoms into two nearly identical halves, and follow how local differences in phase between the halves evolve in time by examining their interference. Initially, the local phases are almost identical, but a rapid decoherence ensues, followed by a very slow further decay. The authors analyze the relative state reached after the initial fast decay and find that it can be described by an equilibrium function with an effective temperature several times less than the initial temperature. Because this cannot be the final state of the system, the authors term the initial process prethermalization.

Conventional surface plasmons have a wave vector exceeding that of light in vacuum, and therefore cannot be directly excited by light that is simply incident on the surface. However, we propose that a plasmon-polariton state can be formed at the boundary between a metal and a dielectric Bragg mirror that can have a zero in-plane wave vector and therefore can be produced by direct optical excitation. In analogy with the electronic states at a crystal surface proposed by Tamm, we call these excitations Tamm plasmons, and predict that they may exist in both the TE and TM polarizations and are characterized by parabolic dispersion relations.

Abstract A system consisting of randomly distributed metallic and dielectric regions is considered. The metal‐non‐metal transition takes place when the volume fraction of the metallic phase approaches the percolation threshold. It is shown that the static dielectric constant diverges near the threshold. Critical indexes are introduced which describe the behaviour of the conductivity and the dielectric constant near the threshold as functions of the volume fraction and frequency. The case of non‐zero dc conductivity of dielectric regions is considered also. It is shown that all indexes describing the critical behaviour of complex conductivity can be expressed by two indexes which are known from computer and model experiments. The results of computer calculations of Webman et al. are analysed.

We present the results of room- and low-temperature measurements of second-order Raman scattering for perfect GaN and AlN crystals as well as the Raman-scattering data for strongly disordered samples. A complete group-theory analysis of phonon symmetry throughout the Brillouin zone and symmetry behavior of phonon branches, including the analysis of critical points, has been performed. The combined treatment of these results and the lattice dynamical calculations based on the phenomenological interatomic potential model allowed us to obtain the reliable data on the phonon dispersion curves and phonon density-of-states functions in bulk GaN and AlN.

CdSe is used as a prototype to show the implications of valence-band degeneracy for the optical properties of strongly quantum-confined nanocrystals. Absorption spectra and photoluminescence spectra obtained under intermediate and strong pulsed excitation show the presence of new structures. The energy levels for the electron and the hole are calculated with the spherical confinement, the nonparabolicity of the conduction band, and the valence band degeneracy taken into account. The oscillator strengths of the dipole-allowed transitions are also calculated. This model is found to be in good agreement with the experimental observations, which originate mainly from the quantization of the energy spectrum of holes with due account given to valence-band degeneracy.

We report ultranarrow $(<0.15\mathrm{meV})$ cathodoluminescence lines originating from single InAs quantum dots in a GaAs matrix for temperatures up to 50 K, directly proving their $\ensuremath{\delta}$-function-like density of electronic states. The quantum dots have been prepared by molecular beam epitaxy utilizing a strain-induced self-organizing mechanism. A narrow dot size distribution of width $12\ifmmode\pm\else\textpm\fi{}1\mathrm{nm}$ is imaged by plan-view transmission electron microscopy. Cathodoluminescence images directly visualize individual dot positions and recombination from a single dot. A dense dot array $(\ensuremath{\sim}{10}^{11}\mathrm{dots}/{\mathrm{cm}}^{2})$ gives rise to a distinct absorption peak which almost coincides with the luminescence maximum.

Piezoelectricity in pyroelectrics and the linear response of polarization to a strain gradient?lexoelectricity) are discussed in the framework of the unified approach. It was pointed out by Born and Huang and by Martin, that there was a difference between the piezoelectric response for the cases of a sound wave and of a uniform strain in a finite crystal, and that only the ``proper'' parts of piezoelectric constants coincided for these cases. It is shown in this paper that there is no such difference if an accurate definition of piezoelectricity is applied. The theory of flexoelectricity in solid crystalline dielectrics is developed. It is shown that the general properties of flexoelectric response strongly differ from those of piezoelectric response: (1) there is an appreciable surface contribution to the flexoelectric response and (2) the bulk flexoelectric responses for the case of a propagating sound wave and for that of a static uniform strain gradient are considerably different. It is proposed to use flexoelectric effect as a method of crystal surface investigation.

We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures--k-cores. The k-core is the largest subgraph where vertices have at least k interconnections. We find the structure of k-cores, their sizes, and their birthpoints--the bootstrap percolation thresholds. We show that in networks with a finite mean number zeta2 of the second-nearest neighbors, the emergence of a k-core is a hybrid phase transition. In contrast, if zeta2 diverges, the networks contain an infinite sequence of k-cores which are ultrarobust against random damage.

Results of detailed investigations of ${\mathrm{Mg}}_{2}{B}^{\mathrm{IV}}$ $({B}^{\mathrm{IV}}=\mathrm{Si},\phantom{\rule{0.3em}{0ex}}\mathrm{Ge},\phantom{\rule{0.3em}{0ex}}\mathrm{Sn})$ compounds and their quasibinary alloys are presented. Our analysis revealed that ${\mathrm{Mg}}_{2}\mathrm{Si}\text{\ensuremath{-}}{\mathrm{Mg}}_{2}\mathrm{Sn}$ system has the most promising for thermoelectric applications combination of transport properties and band structure features. The $n$-type ${\mathrm{Mg}}_{2}{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Sn}}_{x}$ solid solutions were studied in broad range of compositions and electron concentration (up to $5\ifmmode\times\else\texttimes\fi{}{10}^{20}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$). Temperature dependencies of figure of merit were determined in temperature range $300\text{--}870\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ using results of simultaneous measurements of Seebeck coefficient, electrical, and thermal conductivities. The alloy of optimized composition has reproducible figure of merit $Z{T}_{\mathrm{max}}=1.1$. The results of the present study are compared with the data for best modern thermoelectrics.

Electron paramagnetic resonance and Hall measurements show consistently the presence of two donors ( $D1$ and $D2$) in state-of-the-art, nominally undoped ZnO single crystals. Using electron nuclear double resonance it is found that $D1$ shows hyperfine interaction with more than 50 shells of surrounding ${}^{67}\mathrm{Zn}$ nuclei, proving that it is a shallow, effective-mass-like donor. In addition $D1$ exhibits a single interaction with a H nucleus ( ${a}_{H}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.4\phantom{\rule{0ex}{0ex}}\mathrm{MHz}$), thus H is the defining element. It is in agreement with the prediction of Van de Walle [Phys. Rev. Lett. 85, 1012 (2000)] that H acts as a donor in ZnO. The concentration of $D1$ is $6\ifmmode\times\else\texttimes\fi{}{10}^{16}\phantom{\rule{0ex}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ emphasizing its relevance for carrier statistics and applications.

The description of the non-equilibrium dynamics of isolated quantum many-body systems within the framework of statistical mechanics is a fundamental open question. Conventional thermodynamical ensembles fail to describe the large class of systems that exhibit nontrivial conserved quantities, and generalized ensembles have been predicted to maximize entropy in these systems. We show experimentally that a degenerate one-dimensional Bose gas relaxes to a state that can be described by such a generalized ensemble. This is verified through a detailed study of correlation functions up to 10th order. The applicability of the generalized ensemble description for isolated quantum many-body systems points to a natural emergence of classical statistical properties from the microscopic unitary quantum evolution.

Abstract Amorphous semiconductors, being intrinsically metastable in nature, exhibit a wide variety of changes in their physical properties, particularly when photoinduced using bandgap illumination. This article reviews the photoinduced phenomena exhibited by amorphous semiconductors such as amorphous hydrogenated silicon (and other tetrahedrally coordinated materials) and chalcogenide glasses. Features exhibited in common by all types of amorphous semiconductors, whether in the experimentally observed photoinduced metastability or the theoretical models used to account for such behaviour, are stressed.

We find that scale-free random networks are excellently modeled by simple deterministic graphs. Our graph has a discrete degree distribution (degree is the number of connections of a vertex), which is characterized by a power law with exponent gamma=1+ln 3/ln 2. Properties of this compact structure are surprisingly close to those of growing random scale-free networks with gamma in the most interesting region, between 2 and 3. We succeed to find exactly and numerically with high precision all main characteristics of the graph. In particular, we obtain the exact shortest-path-length distribution. For a large network (ln N>>1) the distribution tends to a Gaussian of width approximately sqrt[ln N] centered at (-)l approximately ln N. We show that the eigenvalue spectrum of the adjacency matrix of the graph has a power-law tail with exponent 2+gamma.

Nanoelectronic devices based on 2D materials are far from delivering their full theoretical performance potential due to the lack of scalable insulators. Amorphous oxides that work well in silicon technology have ill-defined interfaces with 2D materials and numerous defects, while 2D hexagonal boron nitride does not meet required dielectric specifications. The list of suitable alternative insulators is currently very limited. Thus, a radically different mindset with respect to suitable insulators for 2D technologies may be required. We review possible solution scenarios like the creation of clean interfaces, production of native oxides from 2D semiconductors and more intensive studies on crystalline insulators.