398 research outputs found

    Native ultrametricity of sparse random ensembles

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    We investigate the eigenvalue density in ensembles of large sparse Bernoulli random matrices. We demonstrate that the fraction of linear subgraphs just below the percolation threshold is about 95\% of all finite subgraphs, and the distribution of linear chains is purely exponential. We analyze in detail the spectral density of ensembles of linear subgraphs, discuss its ultrametric nature and show that near the spectrum boundary, the tail of the spectral density exhibits a Lifshitz singularity typical for Anderson localization. We also discuss an intriguing connection of the spectral density to the Dedekind η\eta-function. We conjecture that ultrametricity is inherit to complex systems with extremal sparse statistics and argue that a number-theoretic ultrametricity emerges in any rare-event statistics.Comment: 24 pages, 9 figure

    Rashba split surface states in BiTeBr

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    Within density functional theory, we study bulk band structure and surface states of BiTeBr. We consider both ordered and disordered phases which differ in atomic order in the Te-Br sublattice. On the basis of relativistic ab-initio calculations, we show that the ordered BiTeBr is energetically preferable as compared with the disordered one. We demonstrate that both Te- and Br-terminated surfaces of the ordered BiTeBr hold surface states with a giant spin-orbit splitting. The Te-terminated surface-state spin splitting has the Rashba-type behavior with the coupling parameter \alpha_R ~ 2 eV\AA.Comment: 8 pages, 7 figure

    Spin-helical Dirac states in graphene induced by polar-substrate surfaces with giant spin-orbit interaction: a new platform for spintronics

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    Spintronics, or spin electronics, is aimed at efficient control and manipulation of spin degrees of freedom in electron systems. To comply with demands of nowaday spintronics, the studies of electron systems hosting giant spin-orbit-split electron states have become one of the most important directions providing us with a basis for desirable spintronics devices. In construction of such devices, it is also tempting to involve graphene, which has attracted great attention because of its unique and remarkable electronic properties and was recognized as a viable replacement for silicon in electronics. In this case, a challenging goal is to make graphene Dirac states spin-polarized. Here, we report on absolutely new promising pathway to create spin-polarized Dirac states based on coupling of graphene and polar-substrate surface states with giant Rashba-type spin-splitting. We demonstrate how the spin-helical Dirac states are formed in graphene deposited on the surface of BiTeCl. This coupling induces spin separation of the originally spin-degenerate graphene states and results in fully helical in-plane spin polarization of the Dirac electrons.Comment: 5 pages, 3 figure

    First principles quasiparticle damping rates in bulk lead

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    First principles calculations of the damping rates (inverse inelastic lifetimes) of low energy quasiparticles in bulk Pb are presented. Damping rates are obtained both for excited electrons and holes with energies up to 8 eV on a set of k vectors throughout the Brillouin zone (BZ). Strong localization effects in the calculated lifetimes are found. Averaged over the BZ inelastic lifetimes versus quasiparticle energy are reported as well. In addition, the effect of the spin-orbit induced splitting in the band structure on the calculated lifetimes in Pb is investigated.Comment: 10 pages, 8 figures, 5 table

    Many-body effects on the Rashba-type spin splitting in bulk bismuth tellurohalides

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    We report on many-body corrections to one-electron energy spectra of bulk bismuth tellurohalides---materials that exhibit a giant Rashba-type spin splitting of the band-gap edge states. We show that the corrections obtained in the one-shot GWGW approximation noticeably modify the spin-orbit-induced spin splitting evaluated within density functional theory. We demonstrate that taking into account many-body effects is crucial to interpret the available experimental data.Comment: 6 pages, 1 figur

    Formation of a single innovation space in the agrarian sector of the EAEU Member States

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    The relevance of the study is determined by the need to form a single innovative space in the agricultural sector of the EAEU Member States in order to make rational use of the aggregate scientific potential of the countries of the Union. Models of interstate cooperation in the scientific and technical sphere were developed and a “panel of indicators” for the development of the market for scientific and technical products was proposed. Practical recommendations on the transfer of innovations in the agricultural sector of the economy of the EAEU member states are given.peer-reviewe

    Pressure on charged domain walls and additional imprint mechanism in ferroelectrics

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    The impact of free charges on the local pressure on a charged ferroelectric domain wall produced by an electric field has been analyzed. A general formula for the local pressure on a charged domain wall is derived considering full or partial compensation of bound polarization charges by free charges. It is shown that the compensation can lead to a very strong reduction of the pressure imposed on the wall from the electric field. In some cases this pressure can be governed by small nonlinear effects. It is concluded that the free charge compensation of bound polarization charges can lead to substantial reduction of the domain wall mobility even in the case when the mobility of free charge carriers is high. This mobility reduction gives rise to an additional imprint mechanism which may play essential role in switching properties of ferroelectric materials. The effect of the pressure reduction on the compensated charged domain walls is illustrated for the case of 180-degree ferroelectric domain walls and of 90-degree ferroelectric domain walls with the head-to-head configuration of the spontaneous polarization vectors.Comment: subm. to PRB. This verion is extended by appendi

    On scale-free and poly-scale behaviors of random hierarchical network

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    In this paper the question about statistical properties of block--hierarchical random matrices is raised for the first time in connection with structural characteristics of random hierarchical networks obtained by mipmapping procedure. In particular, we compute numerically the spectral density of large random adjacency matrices defined by a hierarchy of the Bernoulli distributions {q1,q2,...}\{q_1,q_2,...\} on matrix elements, where qγq_{\gamma} depends on hierarchy level γ\gamma as qγ=pμγq_{\gamma}=p^{-\mu \gamma} (μ>0\mu>0). For the spectral density we clearly see the free--scale behavior. We show also that for the Gaussian distributions on matrix elements with zero mean and variances σγ=pνγ\sigma_{\gamma}=p^{-\nu \gamma}, the tail of the spectral density, ρG(λ)\rho_G(\lambda), behaves as ρG(λ)λ(2ν)/(1ν)\rho_G(\lambda) \sim |\lambda|^{-(2-\nu)/(1-\nu)} for λ|\lambda|\to\infty and 0<ν<10<\nu<1, while for ν1\nu\ge 1 the power--law behavior is terminated. We also find that the vertex degree distribution of such hierarchical networks has a poly--scale fractal behavior extended to a very broad range of scales.Comment: 11 pages, 6 figures (paper is substantially revised
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