Shockley model description of surface states in topological insulators

We show that the surface states in topological insulators can be understood based on a well-known Shockley model, a one-dimensional tight-binding model with two atoms per elementary cell, connected via alternating tunneling amplitudes. We generalize the one-dimensional model to the three-dimensional case corresponding to the sequence of layers connected via the amplitudes, which depend on the in-plane momentum p = (p_x,p_y). The Hamiltonian of the model is described a (2 x 2) Hamiltonian with the off-diagonal element t(k,p) depending also on the out-of-plane momentum k. We show that the complex function t(k,p) defines the properties of the surface states. The surface states exist for the in-plane momenta p, where the winding number of the function t(k,p) is non-zero as k is changed from 0 to 2pi. The sign of the winding number defines the sublattice on which the surface states are localized. The equation t(k,p)=0 defines a vortex line in the three-dimensional momentum space. The projection of the vortex line on the two-dimensional momentum p space encircles the domain where the surface states exist. We illustrate how our approach works for a well-known TI model on a diamond lattice. We find that different configurations of the vortex lines are responsible for the "weak" and "strong" topological insulator phases. The phase transition occurs when the vortex lines reconnect from spiral to circular form. We discuss the Shockley model description of Bi_2Se_3 and the applicability of the continuous approximation for the description of the topological edge states. We conclude that the tight-binding model gives a better description of the surface states.Comment: 18 pages, 17 figures; version 3: Sections I-IV revised, Section VII added, Refs. [33]-[35] added; Corresponds to the published versio

Особенности идеологического механизма государства современной России

Purpose of the study is to determine the range of ideological apparatuses used by the Russian state, the applied set of methods of ideological influence, as well as the features and causes of the ideological orientation of the ruling elite. The work analyses such ideological apparatus of the state as the mass media (newspapers, magazines, TV and radio channels); educational institutions (schools, state educational institutions of higher and secondary vocational education); political parties, public associations, trade unions; film industry (producing and distributing television and film), as well as people of art (filmmakers, writers, artists); church; press and PR services. The features of their relationship with the ruling establishment and the type and content of the used ideological influence are determined. For example, the majority of the media belongs to the media holdings, which in turn are controlled by the economic and political establishment (the state). In addition, there are examples of ideological influence in textbooks, films, public actions. It also briefly describes the "trolling" organizations ("troll factories"), whose activities are aimed at the consciousness of the Internet users. The ruling establishment actively and effectively uses all the possibilities of the ideological apparatus in their class interests. The reason for the lack of a clear and non-vague ideology (like the Soviet one) is, first, the social heterogeneity of the ruling establishment, which also gives rise to different ideological positions, and, second, the opposite situation would only aggravate the legitimacy crisis of the existing political regime. None of the worldview models of the modern ideological spectrum is able to ensure the legitimacy of the ruling establishment, on the one hand, and to eliminate the discrepancies between the declared and social practices, on the other hand.El objetivo del estudio es determinar la gama de aparatos ideológicos utilizados por el estado ruso, el conjunto de métodos de influencia ideológica aplicados, así como las características y causas de la orientación ideológica de la élite gobernante. El trabajo analiza aparatos ideológicos del estado como los medios de comunicación (periódicos, revistas, canales de televisión y radio); instituciones educativas (escuelas, instituciones educativas estatales de educación profesional superior y secundaria); partidos políticos, asociaciones públicas, sindicatos; industria cinematográfica (producción y distribución de televisión y cine), así como personas de arte (cineastas, escritores, artistas); Iglesia; Servicios de prensa y relaciones públicas. Se determinan las características de su relación con el establecimiento gobernante y el tipo y contenido de la influencia ideológica utilizada. Por ejemplo, la mayoría de los medios pertenecen a los medios de comunicación, que a su vez están controlados por el establecimiento económico y político (el estado). Además, hay ejemplos de influencia ideológica en libros de texto, películas, acciones públicas. También describe brevemente las organizaciones de "trolling" ("fábricas de trolls"), cuyas actividades están dirigidas a la conciencia de los usuarios de Internet. El establecimiento gobernante utiliza activa y efectivamente todas las posibilidades del aparato ideológico en sus intereses de clase. La razón de la falta de una ideología clara y no vaga (como la soviética) es, en primer lugar, la heterogeneidad social del establecimiento gobernante, que también da lugar a diferentes posiciones ideológicas, y, en segundo lugar, la situación opuesta solo agravaría La crisis de legitimidad del régimen político existente. Ninguno de los modelos de visión del mundo del espectro ideológico moderno es capaz de garantizar la legitimidad del establecimiento gobernante, por un lado, y eliminar las discrepancias entre las prácticas declaradas y sociales, por otro lado.Цель статьи ‒ изучить особенности идеологического механизма современного российского государства. Проанализированы такие идеологические аппараты государства как средства массовой информации (газеты, журналы, теле- и радио-каналы); учебные заведения (школы, государственные образовательные учреждения высшего и среднего профессионального образования); политические партии, общественные объединения, профессиональные союзы; организации киноиндустрии (производящие и распространяющие теле- и кинофильмы), а также деятели искусств (кинорежиссеры, писатели, художники); церковь; пресс- и PR-службы, информационные отделы государственных органов, использующие Интернет для достижения целей пропаганды, а также специально созданные «троллинговые» организации. Определены особенности их взаимоотношений с правящей элитой, тип и содержание используемого идеологического воздействия. К примеру, большинство средств массовой информации принадлежит медахолдингам, которые в свою очередь подконтрольны экономической и политической элите (государству). Или же между Русской православной церковью и правящей элитой, по-всей видимости, заключено некое соглашение: в обмен на налоговые преференции и субсидии церковь идейно обслуживает интересы элиты. Помимо указанного приведены примеры идеологического воздействия в учебниках, кинофильмах и при помощи публичных действий. Также кратко описана деятельность «троллинговые» организации («фабрики троллей»), чья деятельность направлена на сознание интренет-пользователей. На основе проведенного исследования сделаны несколько выводов: властвующая элита активно и эффективно использует все возможности идеологического аппарата в своих классовых интересах; причина отсутствия четкой и не расплывчатой идеологии (по типу советской), во-первых, в социальной неоднородности правящей элиты, что также порождает несовпадающие идеологические позиции, а, во-вторых, обратное только усугубило бы кризис легитимности существующего политического режима, ведь ни одна из мировоззренческих моделей современного идеологического спектра не в состоянии, с одной стороны, обеспечить легитимность правящей элиты, а с другой ‒ устранить рассогласования между декларируемым и социальной практикой

The growth exponent for planar loop-erased random walk

We give a new proof of a result of Kenyon that the growth exponent for loop-erased random walks in two dimensions is 5/4. The proof uses the convergence of LERW to Schramm-Loewner evolution with parameter 2, and is valid for irreducible bounded symmetric random walks on any two-dimensional discrete lattice.Comment: 62 pages, 7 figures; fixed typos, added reference

Many-body diagrammatic expansion in a Kohn-Sham basis: implications for Time-Dependent Density Functional Theory of excited states

We formulate diagrammatic rules for many-body perturbation theory which uses Kohn-Sham (KS) Green's functions as basic propagators. The diagram technique allows to study the properties of the dynamic nonlocal exchange-correlation (xc) kernel $f_{xc}$. We show that the spatial non-locality of $f_{xc}$ is strongly frequency-dependent. In particular, in extended systems the non-locality range diverges at the excitation energies. This divergency is related to the discontinuity of the xc potential.Comment: 4 RevTeX pages including 3 eps figures, submitted to Phys. Rev. Lett; revised version with new reference

ATP from synaptic terminals and astrocytes regulates NMDA receptors and synaptic plasticity through PSD-95 multi-protein complex

Recent studies highlighted the importance of astrocyte-secreted molecules, such as ATP, for the slow modulation of synaptic transmission in central neurones. Biophysical mechanisms underlying the impact of gliotransmitters on the strength of individual synapse remain, however, unclear. Here we show that purinergic P2X receptors can bring significant contribution to the signalling in the individual synaptic boutons. ATP released from astrocytes facilitates a recruitment of P2X receptors into excitatory synapses by Ca2+-dependent mechanism. P2X receptors, co-localized with NMDA receptors in the excitatory synapses, can be activated by ATP co-released with glutamate from pre-synaptic terminals and by glia-derived ATP. An activation of P2X receptors in turn leads to down-regulation of postsynaptic NMDA receptors via Ca2+-dependent de-phosphorylation and interaction with PSD-95 multi-protein complex. Genetic deletion of the PSD-95 or P2X4 receptors obliterated ATP-mediated down-regulation of NMDA receptors. Impairment of purinergic modulation of NMDA receptors in the PSD-95 mutants dramatically decreased the threshold of LTP induction and increased the net magnitude of LTP. Our findings show that synergistic action of glia- and neurone-derived ATP can pre-modulate efficacy of excitatory synapses and thereby can have an important role in the glia-neuron communications and brain meta-plasticity

Strongly Correlated Electrons on a Silicon Surface: Theory of a Mott Insulator

We demonstrate theoretically that the electronic ground state of the potassium-covered Si(111)-B surface is a Mott insulator, explicitly contradicting band theory but in good agreement with recent experiments. We determine the physical structure by standard density-functional methods, and obtain the electronic ground state by exact diagonalization of a many-body Hamiltonian. The many-body conductivity reveals a Brinkman-Rice metal-insulator transition at a critical interaction strength; the calculated interaction strength is well above this critical value.Comment: 4 pages; 4 figures included in text; Revte

The study of organelle DNA variability in alloplasmic barley lines in the NGS era

Alloplasmic lines are a suitable model for studying molecular coevolution and interrelations between genetic systems of plant cells. Whole chloroplast (cp) and mitochondrial (mt) genome sequences were obtained by the MiSeq System (Illumina). Organelle DNA samples were prepared from a set of 12 alloplasmic barley lines with different cytoplasms of Hordeum vulgare ssp. spontaneum and H. vulgare ssp. vulgare, as well as from their paternal varieties. A bioinformatic approach for analysis of NGS data obtained on an organellar DNA mix has been developed and verified. A comparative study of Hordeum organelle genomes' variability and disposition of polymorphic loci was conducted. Eight types of chloroplast DNA and 5 types of mitochondrial DNA were distinguished for the barley sample set examined. These results were compared with the previous data of a restriction fragment length polymorphism (RFLP) study of organelle DNAs for the same material. Formerly established data about a field evaluation of alloplasmic barley lines were revised in the light of information about organelle genomes gained after NGS. Totally 17 polymorphic loci were found at exons of chloroplast genomes. Seven of the SNPs were located in the genes of the Ndh complex. The nonsynonymous changes of nucleotides were detected in the matK, rpoCI, ndhK, ndhG and infA genes. Some of the SNPs detected are very similar in codon position and in the type of amino acid substitution to the places where RNA editing can occur. Thus, these results outline new perspectives for the future study of nuclear-cytoplasmic interactions in alloplasmic lines