Tunable 3D 2D magnetism in the MnBi2Te4 Bi2Te3 m topological insulators family

Feasibility of many emergent phenomena that intrinsic magnetic topological insulators (TIs) may host depends crucially on our ability to engineer and efficiently tune their electronic and magnetic structures. Here we report on a large family of intrinsic magnetic TIs in the homologous series of the van der Waals compounds (MnBi2Te4)(Bi2Te3)m with m = 0, ⋯, 6. Magnetic, electronic and, consequently, topological properties of these materials depend strongly on the m value and are thus highly tunable. The antiferromagnetic (AFM) coupling between the neighboring Mn layers strongly weakens on moving from MnBi2Te4 (m = 0) to MnBi4Te7 (m = 1) and MnBi6Te10 (m = 2). Further increase in m leads to change of the overall magnetic behavior to ferromagnetic (FM) one for (m = 3), while the interlayer coupling almost disappears. In this way, the AFM and FM TI states are, respectively, realized in the m = 0, 1, 2 and m = 3 cases. For large m numbers a hitherto-unknown topologically nontrivial phase can be created, in which below the corresponding critical temperature the magnetizations of the non-interacting 2D ferromagnets, formed by the MnBi2Te4 building blocks, are disordered along the third direction. The variety of intrinsic magnetic TI phases in (MnBi2Te4)(Bi2Te3)m allows efficient engineering of functional van der Waals heterostructures for topological quantum computation, as well as antiferromagnetic and 2D spintronics.This work is supported by Saint Petersburg State University project for scientific investigations (ID No. 51126254, https://spin.lab.spbu.ru) and Russian Science Foundation (Grant no. 18-12-00062 in part of the photoemission measurements and 18-12-00169 in part of calculations of topological invariants, investigation of dependence of the electronic spectra on SOC strength, and tight-binding band structure calculations). Russian Foundation for Basic Research (Grant nos. 20-32-70179 and 18-52-06009) and Science Development Foundation under the President of the Republic of Azerbaijan (Grant no. EIF-BGM-4-RFTF-1/2017-21/04/1-M-02) are acknowledged. We also acknowledge the support by the Basque Departamento de Educacion, UPV/EHU (Grant no. IT-756-13), Spanish Ministerio de Ciencia e Innovación (Grant no. PID2019-103910GB-I00), the Fundamental Research Program of the State Academies of Sciences (line of research III.23.2.9) and Tomsk State University competitiveness improvement program (project no. 8.1.01.2018). I.P.R. acknowledge support from Ministry of Education and Science of the Russian Federation (State Task No. 0721-2020-0033) (tight-binding calculations). The calculations were performed in Donostia International Physics Center and in the Research park of St. Petersburg State University Computing Center (http://cc.spbu.ru).Peer reviewe

Thallium-based topological insulators from first principles

Resumen del trabajo presentado al 75th Annual Meeting of the DPG and DPG Spring Meeting, celebrado en Dresden (Alemania) del 13 al 18 de marzo de 2011.Currently, there is a substantial interest in topological insulators, which show protected edge-states carrying dissipationless spin currents. Among the new classes of these materials the Tl-based compounds TlAB2 (A=Bi,Sb; B=Se,Te) have attracted considerable interest both on the experimental and theoretical side. We present density functional theory calculations of the bulk materials and their (111) surfaces, displaying protected Dirac-cone shaped surface states together with "trivial" surface states. In contrast to layered materials like Bi2Te3, these compounds are of more three-dimensional character. From the bulk calculations we observe a strong sensitivity of the topological properties on the structural details, that have to be described very accurately. In the surface calculations deeply penetrating Dirac-cone states are observed, calling for careful convergence of the calculations with respect to the film thickness. Similar materials, e.g. the sulfides and InAB2 compounds will be discussed for comparison.Peer reviewe

Bulk and surface electronic structure of SnBi4Te7 topological insulator

Using density functional theory with the spin–orbit coupling included we analyze the bulk and surface electronic structure of SnBi4Te7 ternary compound. It was revealed that this material is a strong topological insulator with a bulk band gap of about 100 meV and a robust surface state around the Γ¯ point. We find that the topological nature of the surface state remains robust with different terminations of the surface.The work was supported by the University of the Basque Country, Departamento de Educación del Gobierno Vasco, and MCyT (grant no. FIS 2004-06490-C03-01).Peer Reviewe

Algorithm for constructing three-dimensional Barcodes to represent nD spatial objects in GIS

В статье рассмотрен алгоритм создания трехмерных Баркодов для представления nD пространственных объектов. Алгоритм основан на методах компьютерной топологии с использованием алгоритма 3D sweep hull для вычисления выпуклых оболочек и триангуляции Делоне. Результатом работы алгоритма являются 3D Баркоды пространственных объектов. Также были построены графики 3D Баркодов, которые отражают их различия во времени. Алгоритм построения 3D Баркодов позволит анализировать пространственные nD объекты в разные временные интервалы. The article describes the algorithm for creating three-dimensional Barcodes to represent nD features. The algorithm is based on computer topology methods using the 3D sweep hull algorithm for computing convex hulls and Delaunay triangulation. The result of the algorithm are 3D Barcodes of features. Were also constructed 3D Barcode graphics, which reflect their differences in time. The algorithm for constructing 3D Barcodes will allow analyzing spatial nD objects at different time intervals.Исследование выполнено при финансовой поддержке РФФИ и администрации Владимирской области в рамках научного проекта № 17-47-330387

A research of classification algorithm of spatial information on the basis of methods of persistent homology and random forest

Проблема классификации пространственных данных является одной из самых сложных в области анализа и обработки пространственной информации. В статье представлен новый подход к решению проблемы классификации пространственных данных. Предлагаемая технология классификации объектов будет базироваться на алгебраической топологии, а именно - на методах персистентной гомологии. В качестве классификатора пространственного объекта взят баркод. Он формируется путем вычисления топологических признаков классифицируемого объекта. Отличительным признаком предлагаемого алгоритма является его инвариантность к аффинным и топологическим преобразованиям. Проведено исследование по результатам работы алгоритма классификации на множестве пространственных объектов различных классов. The classification problem of spatial data is one of the most difficult challenges in the field of the analysis and processing of spatial information. A new approach to a solution of the classification problem of spatial data is presented in article. The offered classification technology of objects will be based on algebraic topology, namely on methods of persistent homology. A barcode is a qualifier of a spatial object. It is determined by computation of topological features of a classified object. The distinctive feature of the offered algorithm is its invariance to affine and topological transformations. The research on results of classification algorithm operation on a set of spatial objects of different classes is carried out.Исследование выполнено при финансовой поддержке администрации Владимирской области согласно договору No326 от 29.09.2017. Исследование выполнено при финансовой поддержке РФФИ и администрации Владимирской области в рамках научного проекта No 17-47-330387

Algorithm for encoding nD spatial objects into GIS

В статье предлагается применить методы компьютерной топологии для создания эффективных структур данных, которые позволят хранить и обрабатывать пространственные сцены в n-мерном пространстве. Основой для представления nD-геообъектов являются n-мерные симплексы. Например, представление пространственных данных высокой размерности позволит описать топологические отношения между 3D-объектами во времени. Разработаны математические основы и программное обеспечение для представления и обработки пространственных данных высокой размерности. Алгоритм кодирования пространственных объектов nD в ГИС предоставит возможность решать широкий круг задач для обработки сложной графической информации. The development of GIS technologies in the modern world is moving towards the use of 3D maps, multiscale, as well as time components. However, today the data of some regularities are kept separately. For high dimensions, those algorithms that work well for 2D and 3D maps are not applicable. The integration of dimensions raises new requirements for creating new methods and algorithms for processing spatial data. The use of topological data analysis is a promising direction in GIS. In this paper, it is proposed to apply computer topology methods to create efficient data structures that will allow storing and processing spatial scenes in a single n-dimensional space. The basis for the representation of nD geoobjects is n-dimensional simplexes. For example, the representation of spatial data of high dimension will allow us to describe the topological relationships between 3D objects in time. There is a need to develop mathematical bases and software for the presentation and processing of spatial data of high dimensionality. The algorithm for encoding nD spatial objects into GIS will provide an opportunity to solve a wide range of tasks for processing complex graphic information.Исследование выполнено при финансовой поддержке РФФИ и администрации Владимирской области в рамках научного проекта № 17-47-330387. Исследование выполнено при финансовой поддержке администрации Владимирской области согласно договору №326 от 29.09.2017