Physics in nonfixed spatial dimensions via random networks.

We investigate the dielectric resonance, local field distribution and effective optical response in the fractal structured metallic-dielectric composites using the Green's function formalism. With the evolution of the fractal level, similarity of the density of states (DOS) of dielectric resonances appears due to the self-similar structure, as well as of the inverse participation ratio (IPR) (which is used to represent the localization of field) of local field, and the effective linear optical responses. For a self-similar defect, when the difference admittance ratio $\ensuremath{\eta}\phantom{\rule{0.2em}{0ex}}[=({ϵ}_{2}\ensuremath{-}{ϵ}_{0})∕({ϵ}_{1}\ensuremath{-}{ϵ}_{0})]⪡0$ or $\ensuremath{\eta}⪢1$, DOS and IPR of the defect modes also exhibit the similarity or antisimilarity. However, for $\ensuremath{\eta}∊(\ensuremath{-}1,2)$, the spectra of DOS and IPR become more complicated as the defect modes overlap the original modes. Finally, the existence of the self-similar defect has no obvious influence on the effective optical responses.

Electronic and magnetic properties of ribbon-shaped nanographite systems with zigzag and armchair edges in a magnetic field are investigated by using a tight-binding model. One of the most remarkable features of these systems is the appearance of edge states, strongly localized near zigzag edges. The edge state in a magnetic field, generating a rational fraction of the magnetic flux $(\ensuremath{\varphi}=p/q)$ in each hexagonal plaquette of the graphite plane, behaves like a zero-field edge state with q internal degrees of freedom. The orbital diamagnetic susceptibility strongly depends on the edge shapes. The reason is found in the analysis of the ring currents, which are very sensitive to the lattice topology near the edge. Moreover, the orbital diamagnetic susceptibility is scaled as a function of the temperature, Fermi energy, and ribbon width. Because the edge states lead to a sharp peak in the density of states at the Fermi level, the graphite ribbons with zigzag edges show Curie-like temperature dependence of the Pauli paramagnetic susceptibility. Hence, there is a crossover from high-temperature diamagnetic to low-temperature paramagnetic behavior in the magnetic susceptibility of nanographite ribbons with zigzag edges.

We report on microscopic measurements of the low-energy electronic structures both at zigzag and armchair edges of bilayer graphene using scanning tunneling microscopy and spectroscopy (STM and STS). We have found that, both in the absence and in the presence of a magnetic field, an almost zero-energy peak in density of states was localized at zigzag edges, as expected for the surface states at zigzag edges of bilayer graphene. In the quantum Hall regime, we have observed clearly Landau levels bending away from the charge neutrality point near both the zigzag and armchair edges. Such a result is a direct evidence for the evolution of Landau levels into the quantum Hall edge states in graphene bilayers. Our experiment indicates that it is possible to explore rich quantum Hall physics in graphene systems using STM and STS.

Presents the first calculations of the electronic density of states, the electrical conductivity and the inverse participation ratio as a function of energy for a large model of hydrogenated amorphous silicon. The model contains 1555 Si atoms and 400 H atoms and all Si atoms are fourfold coordinated. This model has a clear gap in the density of electronic states. The 'mobility gap' (estimated from the conductivity versus energy curves) is about 0.6 eV wider than the gap in the electronic density of states. The authors also present for comparison the same calculations on a defected model of amorphous Si with 1728 atoms which contains states within the gap arising mainly from departure from tetrahedral geometry.

A simple tight-binding model with hopping to the nearest-neighbor sites in the field of attosecond pulse train is considered. A new form of localization, atto-localization, has been obtained. It is checked by simulating as realistically as possible the appropriate hopping in the lattice. This is a drastic change with respect to the Anderson localization. Examinations are performed on an ideal and a disordered lattice. Pair-correlations, density of states, inverse participation ratio and energy level statistics are calculated and verified. The condition under which atto-localization does not appear is also given.

An efficient synthetic method toward graphene‐like molecules (GLMs), having four zigzag edges, is described. They were obtained as stable materials and their structures were confirmed by X‐ray crystallographic analysis. They exhibit topology‐ and size‐dependent electronic properties and global aromaticity, which are all different from GLMs having either all‐armchair edges, or three zigzag edges, or two armchair/two zigzag edges. They can be reversibly oxidized and reduced into stable charged species, which show fragmental aromatic character to minimize anti‐aromaticity. Our studies give some new insights into the electronic structures and properties of a new type of rarely studied GLMs.

From the detailed electronic structure studies on intermetallic compounds, it has been found that these materials have low heat of formation and large glass-forming ability, if the Fermi level falls on the peak in the density of states (DOS) curve. On the other hand, if theE F falls on the pseudogap in the DOS curve, the ordering energy will be larger and the system prefers to form an ordered alloy. The first principles electronic structure calculations performed on Ni3Al show that it is possible to vary the filling of bonding, nonbonding and antibonding states in the DOS curve and this in turn shows gradual structural transformation as well as formation of multiphases by ternary alloying. Possibilities of tailoring the properties of materials by tuning the Fermi level is discussed in this paper.

Discrete- and continuous-time approaches are frequently used to model the role of heterogeneity on dynamical interacting agents on the top of complex networks. While, on the one hand, one does not expect drastic differences between these approaches, and the choice is usually based on one's expertise or methodological convenience, on the other hand, a detailed analysis of the differences is necessary to guide the proper choice of one or another approach. We tackle this problem by investigating both discrete- and continuous-time mean-field theories for the susceptible-infected-susceptible (SIS) epidemic model on random networks with power-law degree distributions. We compare the discrete epidemic link equations(ELE) and continuous pair quenched mean-field (PQMF) theories with the corresponding stochastic simulations, both theories that reckon pairwise interactions explicitly. We show that ELE converges to the PQMF theory when the time step goes to zero. We performed an epidemic localization analysis considering the inverse participation ratio (IPR). Both theories present the same localization dependence on network degree exponent γ: for γ<5/2 the epidemics are localized on the maximum k-core of networks with a vanishing IPR in the infinite-size limit while, for γ>5/2, the localization happens on hubs that do not form a densely connected set and leads to a finite value of the IPR. However, the IPR and epidemic threshold of ELE depend on the time-step discretization such that a larger time step leads to more localized epidemics. A remarkable difference between discrete- and continuous-time approaches is revealed in the epidemic prevalence near the epidemic threshold, in which the discrete-time stochastic simulations indicate a mean-field critical exponent θ=1 instead of the value θ=1/(3-γ) obtained rigorously and verified numerically for the continuous-time SIS on the same networks.

The structures, stabilities, electronic and magnetic properties of fully and partially hydrogenated germanene nanoribbons: A first-principles investigation

The influence of Coulomb interaction on transport properties of spinless electrons in small disordered two-dimensional systems is studied within a tight-binding model. Spatial correlations, inverse participation ratio, and multifractal spectrum of the zero-temperature local tunneling amplitude as well as the dc Kubo conductance are traced as function of the interaction strength U. When U is increased, all of the above quantities are shifted rather smoothly towards localized behavior, indicating the absence of an interaction-driven insulator-metal transition.

Structural, electronic, mechanical, optical and thermoelectric properties of double perovskites A2CuAlCl6 (A=Cs, Rb, K) with direct bandgap using DFT study

A quantum phase transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, which is briefly discussed, presents a second-order ground state phase transition in the thermodynamic (or large particle number) limit, changing from a molecular condensate in one phase to an equilibrium of diatomic molecules–atoms in coexistence in the other one. The usual markers for this phase transition are the ground state energy and the expected value of the number of atoms (alternatively, the number of molecules) in the ground state. In this work, other markers for the QPT, such as the inverse participation ratio (IPR), and particularly, the Rényi entropy, are analyzed and proposed as QPT markers. Both magnitudes present abrupt changes at the critical point of the QPT.

Universal spectral properties of multiplex networks allow us to assess the nature of the transition between disease-free and endemic phases in the SIS epidemic spreading model. In a multiplex network, depending on a coupling parameter, p, the inverse participation ratio (IPR) of the leading eigenvector of the adjacency matrix can be in two different structural regimes: (i) layer-localized and (ii) delocalized. Here we formalize the structural transition point, p*, between these two regimes, showing that there are universal properties regarding both the layer size n and the layer configurations. Namely, we show that IPR ∼ n −δ , with δ ≈ 1, and revealed an approximately linear relationship between p* and the difference between the layers’ average degrees. Furthermore, we showed that this multiplex structural transition is intrinsically connected with the nature of the SIS phase transition, allowing us to both understand and quantify the phenomenon. As these results are related to the universal properties of the leading eigenvector, we expect that our findings might be relevant to other dynamical processes in complex networks.

We revisit two-dimensional particle-hole symmetric sublattice localization problem, focusing on the origin of the observed singularities in the density of states $\ensuremath{\rho}(E)$ at the band center $E=0.$ The most general system of this kind [R. Gade, Nucl. Phys. B 398, 499 (1993)] exhibits critical behavior and has $\ensuremath{\rho}(E)$ that diverges stronger than any integrable power law, while the special random vector potential model of Ludwig et al. [Phys. Rev. B 50, 7526 (1994)] has instead a power-law density of states with a continuously varying dynamical exponent. We show that the latter model undergoes a dynamical transition with increasing disorder---this transition is a counterpart of the static transition known to occur in this system; in the strong-disorder regime, we identify the low-energy states of this model with the local extrema of the defining two-dimensional Gaussian random surface. Furthermore, combining this ``surface fluctuation'' mechanism with a renormalization group treatment of a related vortex glass problem leads us to argue that the asymptotic low-E behavior of the density of states in the general case is $\ensuremath{\rho}(E)\ensuremath{\sim}{E}^{\ensuremath{-}1}{e}^{\ensuremath{-}c|\mathrm{ln}E{|}^{2/3}},$ different from earlier prediction of Gade. We also study the localized phases of such particle-hole symmetric systems and identify a Griffiths ``string'' mechanism that generates singular power-law contributions to the low-energy density of states in this case.

We study the edge states in graphene in the presence of a magnetic field\nperpendicular to the plane of the lattice. Most of the works done so far\ndiscuss the edge states in either zigzag or armchair edge graphene considering\nan isotropic electron hopping. In practice, graphene can have mixture of\narmchair and zigzag edges and the electron hopping can be anisotropic, which is\nthe subject of this article. We predict that the mixed edges smear the enhanced\nlocal density of states (LDOS) at E=0 of the zigzag edge and, on the other\nhand, the anisotropic hopping gives rise to the enhanced LDOS at E=0 in the\narmchair edge. The behavior of the LDOS can be studied using scanning tunneling\nmicroscopy (STM) experiments. We suggest that care must be taken while\ninterpreting the STM data. It is because the clear distinction between the\nzigzag edge (enhanced LDOS at E=0) and armchair edge (suppressed LDOS at E=0)\ncan be lost if the hopping is not isotropic and if the edges are mixed.\n