Majorana fermions in pinned vortices

Exploiting the peculiar properties of proximity-induced superconductivity on the surface of a topological insulator, we propose a device which allows the creation of a Majorana fermion inside the core of a pinned Abrikosov vortex. The relevant Bogolyubov-de Gennes equations are studied analytically. We demonstrate that in this system the zero-energy Majorana fermion state is separated by a large energy gap, of the order of the zero-temperature superconducting gap $\Delta$, from a band of single-particle non-topological excitations. In other words, the Majorana fermion remains robust against thermal fluctuations, as long as the temperature remains substantially lower than the critical superconducting temperature. Experimentally, the Majorana state may be detected by measuring the tunneling differential conductance at the center of the Abrikosov vortex. In such an experiment, the Majorana state manifests itself as a zero-bias anomaly separated by a gap, of the order of $\Delta$, from the contributions of the nontopological excitations.Comment: 9 pages, 2 eps figures, new references are added, several typos are correcte

Instabilities of the AA-stacked graphene bilayer

Tight-binding calculations predict that the AA-stacked graphene bilayer has one electron and one hole conducting bands, and that the Fermi surfaces of these bands coincide. We demonstrate that as a result of this degeneracy, the bilayer becomes unstable with respect to a set of spontaneous symmetry violations. Which of the symmetries is broken depends on the microscopic details of the system. We find that antiferromagnetism is the more stable order parameter. This order is stabilized by the strong on-site Coulomb repulsion. For an on-site repulsion energy typical for graphene systems, the antiferromagnetic gap can exist up to room temperatures.Comment: 4 pages, 2 eps figure, submitted to Phys. Rev. Let

Синтез нових спіроциклічних N-арилзаміщених 2-тіопіримідин-4,6-діонів

A convenient and efficient method for the synthesis of new unsaturated spiro-annulated N-aryl-4,6-dioxopyrimidine-2-thione derivatives has been developed. The resulting compounds can be potential biological active molecules or precursors for further chemical modification.Aim. To develop the methods for the synthesis of new unsaturated spiro-annulated 2-thiopyrimidine-4,6-dione derivatives, which can be used as potentially biological active molecules or precursors for their formation.Results and discussion. By condensation of N-aryl-substituted thioureas and allylmalonic acid using acetic anhydride or acetyl chloride the series of 5-allyl-substituted 2-thiopyrimidinediones has been synthesized. Their further alkylation with allyl bromide or metallyl chloride led to formation of 5,5-dialkenyl derivatives, which were converted to the corresponding unsaturated spirocyclic dioxopyrimidine-2-thiones by ring-closing metathesis. Experimental part. The synthesis of the starting compounds and title products was performed by preparative chemical methods, TLC and column chromatography, elemental analysis, NMR-spectroscopy.Conclusions. The efficient three-step synthetic route of new unsaturated spiro-annulated N-aryl-4,6-dioxopyrimidine-2-thione derivatives from the starting N-arylsubstituted thioureas and allylmalonic acid has been developed. The spiro-annulated products obtained can find application in biological and pharmaceutical science or as starting substrates for further chemical modification.Разработан удобный и эффективный метод синтеза новых ненасыщенных спиро-аннелированных N-арилзамещенных 2-тиопиримидин-4,6-дионов. Полученные соединения могут быть потенциальными биоактивными молекулами или исходными веществами для дальнейшей химической модификации.Цель работы – разработка методов получения новых ненасыщенных спиро-аннелированных производных 2-тиопиримидин-4,6-диона как потенциальных биологически активных соединений или полупродуктов для их получения.Результаты и их обсуждение. Конденсацией N-арилзамещенных тиомочевин и аллилмалоновой кислоты с использованием уксусного ангидрида или ацетилхлорида синтезирован ряд 5-аллилзамещенных 2-тиопиримидиндионов. При их последующем алкилировании аллилбромидом или металлилхлоридом получены 5,5-диалкенильные производные, которые реакциями метатезиса с закрытием цикла были конвертированы в соответствующие непредельные спироциклические диоксопиримидин-2-тионы.   Экспериментальная часть. Синтез исходных соединений и целевых продуктов классическими методами препаративной химии; очистка и идентификация полученных соединений проводились методами тонкослойной и колоночной хроматографии, методом элементного анализа, спектроскопией ЯМР.Выводы. Разработан эффективный трехстадийный путь получения из исходных тиомочевин и аллилмалоновой кислоты новых ненасыщенных спиро-аннелированных производных N-арил-4,6-диоксопиримидин-2-тиона. Полученные спироциклические продукты могут найти применение в биологии и фармацевтической науке, а также использоваться как исходные соединения для дальнейшей химической модификации.Розроблено зручний та ефективний метод синтезу нових ненасичених спіро-анельованих N-арилзаміщених 2-тіопіримідин-4,6-діонів. Одержані сполуки можуть бути потенційними біоактивними молекулами або прекурсорами для подальшої хімічної модифікації. Мета роботи – розробка методів одержання нових ненасичених спіро-анельованих похідних 2-тіопіримідин-4,6-діону як потенційних біологічно активних сполук або напівпродуктів для їх отримання. Результати та їх обговорення. КонденсацієюN-арилзаміщених тіосечовин та алілмалонової кислоти із застосуванням оцтового ангідриду або ацетилхлориду синтезовано серію 5-алілзаміщених 2-тіопіримідиндіонів. При подальшому їх алкілуванні алілбромідом або металілхлоридом одержано 5,5-діалкенільні похідні, які реакціями метатезису із закриттям циклу було перетворено на відповідні ненасичені спіроциклічні діоксопіримідин-2-тіони.Експериментальна частина. Синтез вихідних сполук та цільових продуктів класичними методами препаративної хімії; очистку та ідентифікацію отриманих сполук здійснено методами тонкошарової та колонкової хроматографії, елементним аналізом, ЯМР-спектроскопією.Висновки. Розроблено ефективний тристадійний шлях отримання з вихідних тіосечовин та алілмалонової кислоти нових ненасичених спіро-анельованих похідних N-арил-4,6-діоксопіримідин-2-тіону. Одержані спіроциклічні продукти можуть знайти застосування в біології та фармацевтичній науці, або використовуватись як вихідні сполуки для подальшої хімічної модифікації

Density-density propagator for one-dimensional interacting spinless fermions with non-linear dispersion and calculation of the Coulomb drag resistivity

Using bosonization-fermionization transformation we map the Tomonaga-Luttinger model of spinless fermions with non-linear dispersion on the model of fermionic quasiparticles whose interaction is irrelevant in the renormalization group sense. Such mapping allows us to set up an expansion for the density-density propagator of the original Tomonaga-Luttinger Hamiltonian in orders of the (irrelevant) quasiparticle interaction. The lowest order term in such an expansion is proportional to the propagator for free fermions. The next term is also evaluated. The propagator found is used for calculation of the Coulomb drug resistivity $r$ in a system of two capacitively coupled one-dimensional conductors. It is shown that $r$ is proportional to $T^2$ for both free and interacting fermions. The marginal repulsive in-chain interaction acts to reduce $r$ as compared to the non-interacting result. The correction to $r$ due to the quasiparticle interaction is found as well. It scales as $T^4$ at low temperature.Comment: 5 pages, 1 eps figure; the new version of the e-print corrects an error, which exists in the original submission; fortunately, all important conclusions of the study remain vali

Stem-technologies: mathematics and informatics

Algorithms solutions of tasks in the field of the theory of numbers within implementation of the STEM project are proposed and realized. Calculations in a package of computer algebra on an open code in the environment of Linux DebianПредложены и реализованы алгоритмы решения задач в области теории чисел в рамках реализации проекта STEM. Вычисления в пакете компьютерной алгебры на открытом коде в среде Linux Debia

Experimental (computing) theory of numbers

Carrying out numerical experiments with Euler's function. Specification of the theorem of Mertens. Calculations in a package of computer algebra on an open code in the environment of Linux DebianПроведение численных экспериментов с функцией Эйлера. Уточнение теоремы Мертенса. Вычисления в пакете компьютерной алгебры на открытом коде в среде Linux Debia

Aggregated estimation of the basic parameters of biological production and the carbon budget of Russian terrestrial ecosytems: 2. Net primary production

The estimated net primary production (NPP) of Russian terrestrial ecosystems (annual average over the period from 1988 to 1992) is 9544 Tg of dry matter, or 4353 Tg of carbon. Of the total amount, forests account for approximately 39.2% (here and below, comparisons are made with respect to carbon content); natural grasslands and brushwoods, for 27.6%; farmlands (arable land and cultivated pastures), for 22.0%; and wetlands, for 11.2%. The average NPP density on lands covered with vegetation (1629.8 million hectares in Russia) is 267 g C/m2per year. The highest value (498 g C/m2per year) is characteristic of arable lands. Other land-use/land-cover (LULC) classes have the following NPP densities (in areas covered with vegetation): grasslands and brushwoods, 278 g C/m2; forests, 224 g C/m2; and wetlands, 219 g C/m2per year. In general, Russian terrestrial ecosystems accumulate 59.7% of the total NPP in the aboveground phytomass (47.8% in green parts and 11.9% in wood) and 40.3% in the underground phytomass. The latter parameter differs significantly in different LULC classes and bioclimatic zones. According to calculations, the uncertainty in estimating the total NPP is 11% (a priori confidential probability 0.9)

Teaching English in the higher education institution: teachers and students perspective

The purpose of the given study is to provide description of English for Specific Purposes (ESP) course implementation in Russian higher educational institutions. The authors consider the experience of ESP training at Ogarev Mordovia State University (Saransk, Russia) and outline the most typical issues faced by ESP teachers in real-life conditions of education process. The following problem aspects are pointed out: appropriate selection and use of training materials for the educational course, multilevel groups issue, necessity of due ESP course design etc. The authors also provide the results of the survey for students of some departments of Mordovia Ogarev State University listing the most relevant issues and challenges faced by them while taking an ESP course. The creators of the paper suggest several ways of solution for the issues stated and provide possible directions for the development and quality improvement of ESP courses in the higher education system of Russia

Suspensions of supracolloidal magnetic polymers: self-assembly properties from computer simulations

We study self-assembly in suspensions of supracolloidal polymer-like structures made of crosslinked magnetic particles. Inspired by self-assembly motifs observed for dipolar hard spheres, we focus on four different topologies of the polymer-like structures: linear chains, rings, Y-shaped and X-shaped polymers. We show how the presence of the crosslinkers, the number of beads in the polymer and the magnetic interparticle interaction affect the structure of the suspension. It turns out that for the same set of parameters, the rings are the least active in assembling larger structures, whereas the system of Y- and especially X-like magnetic polymers tend to form very large loose aggregates

Josephson Coupling through a Quantum Dot

We derive, via fourth order perturbation theory, an expression for the Josephson current through a gated interacting quantum dot. We analyze our expression for two different models of the superconductor-dot-superconductor (SDS) system. When the matrix elements connecting dot and leads are featureless constants, we compute the Josephson coupling J_c as a function of the gate voltage and Coulomb interaction. In the diffusive dot limit, we compute the probability distribution P(J_c) of Josephson couplings. In both cases, pi junction behavior (J_c < 0) is possible, and is not simply dependent on the parity of the dot occupancy.Comment: 9 pages; 3 encapsulated PostScript figure