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In the novel stoichiometric iron-based material RbEuFe4As4 superconductivity coexists with a peculiar long-range magnetic order of Eu 4f states; their coexistance is puzzling and represents a challenge for both experiment and theory. Using angle-resolved photoemission spectroscopy, resonant photoemission spectroscopy, Andreev reflection spectroscopy and scanning tunneling spectroscopy we have addressed this puzzle and unambigously shown that Fe- and Eu-derived states are largely decoupled and that superconducting and a long range magnetic orders exist almost independently from each other.

Using density functional theory, we propose the (MnSb2Te4)·(Sb2Te3)n family of stoichiometric van der Waals compounds that harbor multiple topologically nontrivial magnetic phases. In the ground state, the first three members of the family (n = 0, 1, 2) are 3D antiferromagnetic topological insulators, while for n ≥ 3 a special phase is formed, in which a nontrivial topological order coexists with a partial magnetic disorder in the system of the decoupled 2D ferromagnets, whose magnetizations point randomly along the third direction. Furthermore, due to a weak interlayer exchange coupling, these materials can be field-driven into the FM Weyl semimetal (n = 0) or FM axion insulator states (n ≥ 1). Finally, in two dimensions, we reveal these systems to show intrinsic quantum anomalous Hall and AFM axion insulator states, as well as quantum Hall state, achieved under external magnetic field. Our results demonstrate that MnSb2Te4 is not topologically trivial as was previously believed that opens possibilities of realization of a wealth of topologically nontrivial states in the (MnSb2Te4)·(Sb2Te3)n family., M.M.O. acknowledges the support by the Spanish Ministerio de Ciencia e Innovación (Grant No. PID2019-103910GB-I00). E.V.C. acknowledges the Saint Petersburg State University Project for Scientific Investigations (ID No. 51126254, https://spin.lab.spbu.ru). S.V.E. acknowledges support by the Russian Science Foundation (Grant No. 18-12-00169-p). Y.M.K. acknowledges support from a government research assignment for ISPMS SB RAS (Project FWRW-2019-0032) for the FLEUR calculations. I.P.R. acknowledges support from the Ministry of Education and Science of the Russian Federation (State Task No. 0721-2020-0033) for the tight-binding calculations. A.E. acknowledges support from OeAD Grant No. HR 07/2018 for the HUTSEPOT calculations.

In pnictide RbEuFe4As4, superconductivity sets in at 36 K and coexists, below 15-19 K, with the long-range magnetic ordering of Eu 4f spins. Here we report scanning tunneling experiments performed on cold-cleaved single crystals of the compound. The data revealed the coexistence of large Rb-Terminated and small Eu-Terminated terraces, both manifesting 1 × 2 and 2×2 reconstructions. On 2×2 surfaces, a hidden electronic order with a period â 5 nm was discovered. A superconducting gap of â 7 meV was seen to be strongly filled with quasiparticle states. The tunneling spectra compared with density functional theory calculations confirmed that flat electronic bands due to Eu 4f orbitals are situated â 1.8 eV below the Fermi level and thus do not contribute directly to Cooper pair formation.

The Jahn–Teller effect is a geometrical distortion which lowers the system symmetry and lifts orbital degeneracy in molecules and solids. It affects a wide range of properties, including magnetic and band structures. In this work we propose a family of Cr-containing intrinsic magnetic topological insulator materials which are subjected to a pseudo-Jahn–Teller effect—CrBi2Se4, CrBi2Te2Se2, and CrBi2Te4. Using first-principles calculations we study their properties and investigate the impact of Jahn–Teller distortions on the electronic and magnetic properties. We show that these distortions can significantly affect magnetic anisotropy energy and band structure. Without the distortions accounted for, all three of the compounds exhibit a semimetallic band structure. The distortions open a band gap, which in the cases of CrBi2Te2Se2 and CrBi2Te4 is inverted. We also investigate the CrBi2Te2Se2 and CrBi2Te4 surface band structure and demonstrate that the surface states have a topological origin.

Mechanisms of atomic layer-by-layer formation of the equilibrium structure of multilayer Na film on the Cu(001) surface have been studied taking into account relaxation and dynamic (phonon) processes. It has been shown that the atomic rearrangement of the substrate-commensurate с(2 × 2) superstructure of the first Na monolayer to a bcc (110)-oriented structure begins with the second monolayer. The dynamic contribution to the formation of the structure of the growing Na film has been estimated. It has been shown that phonon modes select exponentially observed structures from statically favorable structures. All calculations have been performed with interatomic potentials constructed with the embedded atom method. The comparison of the calculated vibrational frequencies with the existing experimental data has demonstrated their good agreement., This work was supported by the Siberian Branch, Russian Academy of Sciences (project no. III.23.2.9, basic research program for 2019–2021). The numerical calculations were supported by the Mendeleev Foundation, Tomsk State University (project no. 8.1.01.2018). We are grateful to Prof. G. Benedek for stimulating discussion.

We present a theoretical investigation of electron states hosted by magnetic domain walls on the three-dimensional topological insulator surface. The consideration includes the domain walls with distinct vectorial and spatial textures. The study is carried out on the basis of the Hamiltonian for quasirelativistic fermions by using a continual approach and tight-binding calculations. We derive the spectral characteristics and spatial localization of the one-dimensional low-energy states appearing at the domain walls. The antiphase domain walls are shown to generate the topologically protected chiral states with linear dispersion, the group velocity and spin-polarization direction of which depend on an easy-axis orientation. In the case of an easy-plane anisotropy, we predict a realization of a dispersionless state flatband in the energy spectrum, that is spin polarized along the surface normal. Modification of the surface states in the multidomain case, which is approximated by a periodic set of domain walls, is described as well. We find that the magnetic domain walls with complex internal texture, such as N\'eel-like or Bloch-like walls, also host the topological states, although their spectrum and spin structure can be changed compared with the sharp wall case.

Inelastic interactions of quantum systems with the environment usually wash coherent effects out. In the case of Friedel oscillations, the presence of disorder leads to a fast decay of the oscillation amplitude. Here we show both experimentally and theoretically that in three-dimensional topological insulator Bi2Te3 there is a nesting-induced splitting of coherent scattering vectors which follows a peculiar evolution in energy. The effect becomes experimentally observable when the lifetime of quasiparticles shortens due to disorder. The amplitude of the splitting allows an evaluation of the lifetime of the electrons. A similar phenomenon should be observed in any system with a well-defined scattering vector regardless of its topological properties.

Electron-phonon interaction in the Si(111)-supported rectangular phases of In is investigated within the density-functional theory and linear-response. For both single-layer and double-layer structures, it is found that the phonon-induced scattering of electrons is almost exclusively determined by vibrations of In atoms. It is shown that the strength of electron-phonon coupling at the Fermi level λ(EF) increases almost twofold upon adding the second In layer. One of the reasons is that additional low-frequency modes appear in the phonon spectrum, which favors a strong enhancement of λ(EF). The agreement of the calculated parameter λ(EF) = 0.99 for a double-layer structure as well as the superconducting transition temperature Tc = 3.5 K with experimental estimates indicates that the discovered superconducting phase is probably a double-layer rectangular -In structure on Si(111) with a coverage of 2.4 ML. This conclusion is also supported by good agreement between the calculated electron band structure and ARPES measurements.

Closed-shell atoms scattered from a metal surface exchange energy and momentum with surface phonons mostly via the interposed surface valence electrons, i.e., via the creation of virtual electron-hole pairs. The latter can then decay into surface phonons via electron-phonon interaction, as well as into acoustic surface plasmons (ASPs). While the first channel is the basis of the current inelastic atom scattering (IAS) surface-phonon spectroscopy, no attempt to observe ASPs with IAS has been made so far. In this study we provide evidence of ASP in Ni(111) with both Ne atom scattering and He atom scattering. While the former measurements confirm and extend so far unexplained data, the latter illustrate the coupling of ASP with phonons inside the surface-projected phonon continuum, leading to a substantial reduction of the ASP velocity and possibly to avoided crossing with the optical surface phonon branches. The analysis is substantiated by a self-consistent calculation of the surface response function to atom collisions and of the first-principle surface-phonon dynamics of Ni(111). It is shown that in Ni(111) ASP originate from the majority-spin Shockley surface state and are therefore collective oscillation of surface electrons with the same spin, i.e. it represents a new kind of collective quasiparticle: a Spin Acoustic Surface Plasmon (SASP)., The work of I.V.S. is supported by the Ministry of Science and Higher Education of the Russian Federation for funding in framework of State Task (No. 0721-2020-0033). V.M.S. and P.M.E. acknowledge support from the Spanish Ministry of Science and Innovation (Grant No. PID2019-105488GB-I00) and D.F. from Grant No. PID2019-109525RB-I00. E.V.C. acknowledges support from Saint Petersburg State University (project ID No. 51126254). R.M. and D.F. acknowledge financial support from the Spanish Ministry of Economy and Competitiveness, through the “María de Maeztu” Programme for Units of Excellence in R&D (CEX2018-000805-M). IMDEA Nanociencia acknowledges support from the ’Severo Ochoa’ Programme for Centres of Excellence in R&D (MINECO, Grant SEV-2016-0686). Part of the calculations was performed at the SKIF-Cyberia supercomputer at the National Research Tomsk State University (Russian Federation) and the Supercomputer Center of D.I.P.C. (Spain).

Discovered in 1962, the divalent ferromagnetic semiconductor EuS (TC = 16.5 K, Eg = 1.65 eV) has remained constantly relevant to the engineering of novel magnetically active interfaces, heterostructures, and multilayer sequences and to combination with topological materials. Because detailed information on the electronic structure of EuS and, in particular, its evolution across TC is not well-represented in the literature but is essential for the development of new functional systems, the present work aims at filling this gap. Our angle-resolved photoemission measurements complemented with first-principles calculations demonstrate how the electronic structure of EuS evolves across a paramagnetic–ferromagnetic transition. Our results emphasize the importance of the strong Eu 4f–S 3p mixing for exchange-magnetic splittings of the sulfur-derived bands as well as coupling between f and d orbitals of neighboring Eu atoms to derive the value of TC accurately. The 4f–3p mixing facilitates the coupling between 4f and 5d orbitals of neighboring Eu atoms, which mainly governs the exchange interaction in EuS., This work was supported by the German Research Foundation (DFG) through Grant No. KR3831/5-1, No. LA655/20-1, No. SFB1143 (Project No. 247310070), and No. TRR288 (422213477, project A03). We acknowledge support from the Russian Foundation for Basic Research (Grant No. 20-32-70127) and Saint-Petersburg State University (Grant No. ID 73028629). S.V.E. acknowledges support from a government research assignment for ISPMS SB RAS (Project FWRW-2019-0032). We acknowledge MAX-IV Laboratory for time on the Bloch Beamline under Proposal 20190824. Research conducted at MAX IV, a Swedish national user facility, is supported by the Swedish Research council under contract 2018-07152, the Swedish Governmental Agency for Innovation Systems under contract 2018-04969, and Formas under contract 2019-02496. The research has also been supported by the project CALIPSO plus under Grant Agreement 730872 from the EU Framework Programme for Research and Innovation HORIZON 2020.

Narrow-gap semiconductors with strong spin-orbit coupling such as bismuth tellurohalides have become popular candidates for spintronic applications. But driving spin-polarized photocurrents in these materials with circularly polarized light requires picosecond lifetimes of the photoexcited carriers and low spin-flip scattering rates. In search of these essential ingredients, we conducted an extensive study of the carrier dynamics on the Te-terminated surface of BiTeI, which exhibits a giant Rashba splitting of both surface and bulk states. We observe a complex interplay of surface and bulk dynamics after photoexcitation. Carriers are rapidly rearranged in momentum space by quasielastic phonon and defect scattering, while a phonon bottleneck leads to a slow equilibration between bulk electrons and lattice. The particular band dispersion opens an inelastic decay channel for hot carriers in the form of plasmon excitations, which are immanent to Rashba-split systems. These ultrafast scattering processes effectively redistribute excited carriers in momentum and energy space and thereby inhibit spin-polarized photocurrents., This project was supported by the German Research Foundation via the Collaborative Research Center TRR 227 on Ultrafast Spin Dynamics, project A1, and the German-Russian Interdisciplinary Science Center (GRISC). A.S.K. is indebted to the International Max Planck Research School Functional Interfaces in Physics and Chemistry for financial support. B.A. and V.V. acknowledge travel support by GRISC. O.E.T. and K.A.K. were supported by the Russian Science Foundation (Project No. 17-12-01047) and a state contract of ISP and IGM SB RAS. A.S. acknowledges support by Russian Science Foundation (Grant No. 18-12-00062). A.S. and E.V.C. acknowledge support by the Saint Petersburg State University (Grant No. ID 73028629).

This article is part of the themed collection: Festschrift for Peter Toennies - New Horizons in the Dynamics of Molecules: from Gases to Surfaces., The structure and magnetic properties of small Cr clusters, Cr3 and Cr4, adsorbed on the Cu(111) surface have been investigated using density functional theory (DFT) calculations and their vibrational properties have been studied within calculations based on tight-binding second moment approximation interatomic interaction potentials (TBSMA). It has been shown that the magnetic ordering in the Cr clusters significantly affects their crystal structure and symmetry, which influences the vibrational modes of the clusters and nearest neighbor copper atoms. In turn, these modes select potentially possible structures of Cr3 and Cr4, prohibiting the lowest total energy cluster structure as dynamically unstable., This work was supported by the Government Research assignment for ISPMS SB RAS, Project No. III.23.2.9. E. V. C. acknowledges partial support from Saint Petersburg State University (Grant No. ID 51126254).

The anisotropy of the quasiparticle lifetime in the layered tungsten dichalcogenide WSe is studied for energies up to 90 eV above the Fermi level. The inverse lifetime is calculated within the GW approximation based on a full energy and momentum dependent ab initio dielectric function of WSe and wave functions calculated by the plane wave pseudopotential method. The relation between the energy loss function and the quasiparticle lifetime is analyzed. The electron mean free path for three propagation directions ΓA, ΓK, and ΓM was obtained by including the inverse lifetime as an absorbing potential into the Schrödinger equation and calculating the electron scattering by the surface. The inverse quasiparticle lifetime is found to grow steadily and smoothly with energy, and, in spite of the highly anisotropic geometry, to be very similar for the three directions. At the same time, the mean free path is found to vary non-monotonically with energy and to show significant anisotropy., We acknowledge funding from the project PI2017-30 of the Departamento de Educación, Política Lingüística y Cultura of the Basque government, the University of the Basque Country UPV/EHU (Grant no. IT-756-13), and the Spanish Ministry of Economy, Industry and Competitiveness MINEICO (Project no. FIS2016-76617-P).

The computational modeling within a density functional theory was applied for simulations of electronic spectra and calculations of structural and energy characteristics of the cubic double perovskite oxides Sr2Mg1−xNixMoO6–δ, where x = 0, 0.5, and 1. The oxygen stoichiometric molybdates are antiferromagnetic semiconductors with an energy gap near 2 eV. The energy-based arguments show that anti-site cation disorder may contribute to the structural stability of the molybdates. It is found that nickel doping is favorable for mitigated chemical expansion. The replacement of magnesium by nickel is accompanied by the contribution of Ni3d states to the valence band while leaving hybrid Mo4d-O2p states in the conduction band virtually unchanged. It is shown that the compounds under study are thermodynamically unstable in heavily reducing conditions which is confirmed by experimental results. The appearance of oxygen deficiency in Sr2Mg1−xNixMoO6–δ results in the formation of oxygen vacancy associated donor states near the bottom of the conduction band and the transition from the intrinsic to degenerate semiconductor. It is suggested that the influence of nickel dopants on the energy and density of the donor states may help to explain variations of the conducting properties with doping level.

Based on the relativistic spin-polarized density functional theory calculations we investigate the crystal structure, electronic and magnetic properties of a family MnPn 2 Ch 4 compounds, where pnictogen metal atoms ( Pn ) are Sb and Bi; chalcogens ( Ch ) are Se, Te. We show that in the series the compounds of this family with heavier elements prefer to adopt rhombohedral crystal structure composed of weakly bonded septuple monoatomic layers while those with lighter elements tend to be in the monoclinic structure. Irrespective of the crystal structure all compounds of the MnPn 2 Ch 4 series demonstrate a weak energy gain (of a few meV per formula unit or even smaller than meV) for antiferromagnetic (AFM) coupling for magnetic moments on Mn atoms with respect to their ferromagnetic (FM) state. For rhombohedral structures the interlayer AFM coupling is preferable while in monoclinic phases intralayer AFM configuration with ferromagnetic ordering along the Mn chain and antiferromagnetic ordering between the chains has a minimum energy. Over the series the monoclinic compounds are characterized by substantially wider bandgap than compounds with rhombohedral structure.

The electronic structure and topological properties of the AIIMg2Bi2 (AII = Mg,Ca,Sr,Ba) compounds are theoretically studied with the use of exact exchange. It is found that the MgBi compound in the equilibrium state is a semimetal, whereas three other compounds are semiconductors with a direct fundamental band gap. It is predicted that the uniaxial deformation of three-component compounds results in transitions to topologically nontrivial phases: topological insulator and topological and Dirac semimetals. Owing to such a rich variety of topologically nontrivial phases, these compounds may be of interest for further theoretical and experimental studies., This work was supported by Tomsk State University (project no. 8.1.05.2015, program Mendeleev Scientific Foundation), by St. Petersburg State University (project no. 15.61.202.2015), by the Russian Foundation for Basic Research (project no. 15-02-02717-а), and by the Ministry of Education and Science of the Russian Federation (project no. 3.9003.2017/P220).

The effect of spin-orbit coupling on quantum well states (QWSs) in atomically thin Ir adlayers deposited on the Au(111) substrate is studied in the framework of the density functional theory. Varying the Ir film thickness from 1 to 3 atomic layers, we find numerous Ir-derived QWSs, which are mainly of d character. The resulting band dispersion of QWSs appearing around the surface Brillouin zone center in a wide Au(111) energy gap is analyzed in the framework of the Rashba model. In all such QWSs, the fitted values of the Rashba parameter exceed 2eVÅ. The maximal value of 6.4eVÅ was obtained for the 1-monolayer-Ir/Au(111) system. We explain such large spin splitting by hybridization between different QWSs. Strong enhancement is observed in the density of electronic states at the surface in the energy region around the Fermi level caused by these QWSs., I.V.S. acknowledges the Ministry of Science and Higher Education of the Russian Federation for funding in framework of State Task (No. 0721-2020-0033). Y.M.K. acknowledges the Fundamental Research Program of the State Academies of Sciences, line of research III.23.2.9 and the Tomsk State University competitiveness improvement program (Project No. 8.1.01.2018). V.M.S. acknowledges funding from the Project of the Basque Government (Q-NANOFOT IT1164-19). E.V.C. acknowledges the Saint-Petersburg State University (Project No. 51126254). V.M.S. and E.V.C. acknowledge the Spanish Ministry of Economy, Industry and Competitiveness MINEICO (Projects Nos. FIS2016-76617-P and FIS2016-75862-P).

The spectrum of electromagnetic collective excitations in Dirac semimetals placed in a quantizing magnetic field is considered. We have found the Landau damping regions using the energy and momentum conservation law for allowed transitions between one-particle states of electron excitations. Analysis of dispersion equations for longitudinal and transverse waves near the window boundaries in the Landau damping regions reveals different types of collective excitations. We also indicate the features of universal broadening of cyclotron absorption for a magnetic field variation in systems with linear dispersion of the electron spectrum. The use of the obtained spectrum also allows us to predict a number of oscillation and resonance effects in the field of magneto-optical phenomena., This work was supported in part by Project No. 18-12-00169 of the Russian Science Foundation.

Modification of the gap at the Dirac point (DP) in axion antiferromagnetic topological insulator MnBi2Te4 and its electronic and spin structure have been studied by angle- and spin-resolved photoemission spectroscopy (ARPES) under laser excitation at various temperatures (9–35 K), light polarizations and photon energies. We have distinguished both large (60–70 meV) and reduced (, The authors acknowledge support by the Saint Petersburg State University (Grant No. 51126254), Russian Science Foundation (Grant No. 18-12-00062 in part of the photoemission measurements and Grant No. 18-12-00169 in part of the electronic band structure calculations) and by Russian Foundation of Basic Researches (Grants Nos. 18-52-06009 and 20-32-70179) and Science Development Foundation under the President of the Republic of Azerbaijan (Grant No. EI F-BGM-4-RFTF1/2017-21/04/1-M-02). A. Kimura was financially supported by KAKENHI (Grants No. 17H06138, No. 17H06152, and No. 18H03683). S.V.E. and E.V.C. acknowledge support by the Fundamental Research Program of the State Academies of Sciences (line of research III.23.2.9). The authors kindly acknowledge the HiSOR staff and A. Harasawa at ISSP for technical support and help with the experiment. The ARPES measurements at HiSOR were performed with the approval of the Proposal Assessing Committee (Proposal Numbers: 18BG027 and 19AG048). XAS and XMCD measurements were performed at BL23SU of SPring-8 (Proposal Nos. 2018A3842 and 2018B3842) under the Shared Use Program of JAEA Facilities (Proposal Nos. 2018A-E25 and 2018B-E24) with the approval of Nanotechnology Platform project supported by MEXT, Japan (Proposal Nos. A-18-AE-0020 and A-18-AE-0042). M. M. Otrokov acknowledges the support by Spanish Ministerio de Ciencia e Innovacion (Grant no. PID2019-103910GB-I00). K. Yaji was financially supported by KAKENHI (Grants No. 18K03484).

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).

This work is supported by the Russian Science Foundation (Grants No. 18-12-00169 in part of the density functional calculations and No. 18-12-00062 in part of the photoemission measurements) and Saint Petersburg State University (Grant ID 40990069). The support from the Academic D.I. Mendeleev Fund Program of Tomsk State University (Project No. 8.1.01.2018), the Russian Foundation for Basic Researches (Grant No. 18-52-06009), the Science Development Foundation under the President of the Republic of Azerbaijan (Grant No. EIF/MQM/Elm-Tehsil-1-2016-1(26)-71/01/4-M33), the Basque Country Government, Departamento de Educacion, Universidades e Investigacion (Grants No. IT-756-13 and No. IT1301-19) and the Spanish Ministerio de Ciencia e Innovacion (Grant No. FIS2016-75862-P) are acknowledged. J.S.-B. gratefully acknowledges financial support from the Impuls-und Vernetzungsfonds der Helmholtz-Gemeinschaft under Grant No. HRSF-0067 (Helmholtz-Russia Joint Research Group). Calculations were partly performed using computational resources provided by Resource Center “Computer Center of SPbU” (http://cc.spbu.ru) and the SKIFCyberia sup

The magnetic properties of single- and multicomponent trimers of heavy p-elements of Groups IV-VI (Pb, Bi, Te) with a pronounced relativistic effect, as well as their anions and cations, are studied. Spin and orbital magnetic moments of the considered clusters are calculated using the formalism of the density functional theory. For most clusters, calculations reveal nonzero magnetic moments. It is shown that the spin-orbit coupling significantly affects the spin magnetic moment in such clusters. The energy of magnetic anisotropy is calculated for all neutral and charged trimers and the direction of the easy magnetization axis is determined.

Within density functional theory we study the bulk band structure and surface states of bismuth oxychalcogenides Bi2O2Se and Bi2O2Te. We consider both polar and nonpolar surface terminations. On the basis of relativistic ab initio calculations, we show that both unreconstructed (polar) and reconstructed (nonpolar) surfaces possess the Rashba spin-split surface states. The metallic Rashba-split states on polar surfaces stem from huge potential bending, positive or negative, depending on surface polarity. On the nonpolar surfaces resulting from single-crystal cleavage the emerging Rashba-split states are nonmetallic., This work was supported by the Fundamental Research Program of the State Academies of Sciences, line of research III.23, and the Academic D. I. Mendeleev Fund Program of Tomsk State University (Project No. 8.1.01.2018). The support from the Saint Petersburg State University (Project No. 15.61.202.2015), Basque Country Government, Departamento de Educación, Universidades e Investigación (Grant No. IT-756-13), and the Spanish Ministry of Science and Innovation (Grant No. FIS2016-75862-P) is also acknowledged. Calculations were performed using computational resources provided by Resource Center “Computer Center of SPbU” and the SKIF-Cyberia supercomputer at the National Research Tomsk State University. S.V.E. thanks I. A. Nechaev for fruitful discussions.

The absorption of electromagnetic radiation in Dirac semimetals in a quantizing magnetic field has been considered. A universal broadening of the collisionless cyclotron damping line of electromagnetic waves at a decrease in the number of filled Landau levels has been revealed. New regimes of the propagation of electromagnetic waves and new accompanying effects have been found., This work was supported in part by the Russian Science Foundation (project no. 18-12-00169).

We report a theoretical study of the spin-dependent transport properties in heterostructures containing a three-dimensional topological insulator (TI) thin film and ferromagnetic normal insulator (FMNI) slab. Within the framework of a continual approach for the FMNI/TI/FMNI trilayer model, we reveal how the magnetic proximity effect at the TI/FMNI interface can influence an intrinsic Hall response of the system. We predict that the FMNI/TI/FMNI trilayer undergoes a transition into the quantum anomalous Hall phase either from the topologically trivial phase or from the quantum spin Hall phase, which is controlled by tuning the proximity-induced exchange field, the TI film thickness, and the TI band structure parameters. We draw the corresponding phase diagram of the FMNI/TI/FMNI trilayer. Moreover, we argue that the roughness at the TI/FMNI interfaces can cause the decomposition of the TI film into topologically distinct domains, which affects the Hall conductivity. We discuss the specifics of manifestation and complexities of observation of quantized conductivity in realistic TI/FMNI heterostructures., We acknowledge partial support from the Basque Country Government, Departamento de Educación, Universidades e Investigación (Grant No. IT-756-13), the Spanish Ministry of Science and Innovation (Grant No. FIS2016-75862-P), the Tomsk State University Academic D.I. Mendeleev Fund Program (Grant No. 8.1.05.2015), Saint Petersburg State University (Grant No. 15.61.202.2015), Russian Science Foundation (Grant No. 18-12-000169), and Russian Foundation for Basic Research (Grant No. 16-02-00024).

Equilibrium lengths and binding energies, vibrational frequencies, width of the HOMO–LUMO gap, and the magnetic anisotropy energies for one- and two-component dimers of heavy p elements of Groups IV (Sn, Pb), V (Sb, Bi), and VI (Se, Te) with a pronounced relativistic effect have been calculated with the use of the formalism of the density functional theory. It has been shown that it is necessary to take into account the spin–orbit coupling, which significantly affects the energy parameters of clusters. The analysis of the data obtained has revealed that the Pb–Te, Pb–Se, Sn–Te, and Sn–Se dimers have the widest gap at the Fermi level and the lowest reactivity. The magnetic anisotropy energy has been calculated for all single- and doublecomponent dimers and the direction of the easy magnetization axis has been determined., This work was performed within the Program of Basic Scientific Research for State Academies of Sciences for 2013–2020 and was supported by the Russian Foundation for Basic Research (project no. 15-02-02717-a).

A new method for the synthesis of various types of copper(II) formates with Cu(NO3)2∙3H2O and formic acid, orthorhombic (α) and monoclinic (β) modifications of anhydrous copper(II) formate, as well as Cu(HCOO)2∙2H2O and Cu(HCOO)2∙4H2O. The identity of the obtained compounds was confirmed by X-ray phase analysis, optical microscopy and thermogravimetry methods. It was shown that Cu(HCOO)2∙4H2O can be used as a precursor for producing copper powders with particle size of the order of 150 nm. The results of investigation of vibration and absorption spectra of α and β modifications of anhydrous copper(II) formate are presented. Their magnetic behavior in the temperature interval 2–300 K was estimated, and comparative analysis of magnetic properties was carried out. First-principle calculations of electronic band structure for anhydrous α and β modifications were performed. The results obtained correspond to experimentally observed structural instability of β-Cu(HCOO)2, fundamental absorption edge enhancement during transition from α to β modification, and low-temperature ferromagnetic ordering in α-Cu(HCOO)2. Simulation for β modification is indicative of antiferromagnetic ordering of magnetic moments inside chains formed by copper-oxygen octahedra.

The topical problem of realization of the proper transverse conductivity in magnetic heterostructures based on topological insulators has been discussed. Our recent theoretical studies developing a universal approach to analytically simulate the quantum anomalous Hall effect at various ways for introducing a magnetic order into a topological insulator film have been briefly reviewed. Our model involves a consistent description of electronic states of the system, which determine the quantum anomalous Hall effect, with the reduction of the dimension from three-dimensional bulk through two-dimensional interface to one-dimensional edge. This makes it possible to emphasize the particular role of physical boundaries such as interfaces and side faces for spin-dependent transport in heterostructures. A number of new results recently obtained within the proposed approach have been reported. The data of recent experiments with new magnetic materials and structures have been discussed in terms of our theoretical results., This work was supported by the Russian Science Foundation (project no. 18-12-00169), by the St. Petersburg State University (project no. Pure ID 40990069), by the National Research Tomsk State University (project no. 8.1.01.2018, program “Mendeleev Science Foundation”), and by the Russian Foundation for Basic Research (project no. 18-52-06009).

We present a theoretical investigation of the structural and vibrational properties of ordered 2D phases formed by the Li, Na and K atoms on the Cu(0 01) surface. The lattice relaxation, phonon dispersions and polarization of vibrational modes as well as the local density of states are calculated using the embedded-atom method. The obtained structural parameters and vibrational frequencies are in close agreement with available experimental results., This work was performed within the frame of the Fundamental Research Program of the State Academies of Sciences for 2013–2020, line of research III.23. We also acknowledge the support from the Academic D I Mendeleev Fund Program of Tomsk State University (Project No. 8.1.01.2018).

New semimetal systems along with Dirac and Weyl semimetals contain compounds, in which the energy of electron excitations vanishes not at nodes but on lines. A higher dimension of the degeneracy space changes many physical properties. We consider a chain of loops consisting of Dirac spectrum nodes in nonsymmorphic crystalline compounds placed in external mutually perpendicular magnetic and electric fields. An exact solution for the spectrum is obtained under the assumption of particle-hole symmetry. An analysis of this spectrum shows the existence of a line of critical values of the magnetic and electric fields, at which a quantum phase transition to a gapless state occurs. The use of the obtained spectrum allows also predicting a number of new oscillation and resonance effects in the field of magneto-optical phenomena., This work was supported in part by Project No. 3.2637.2017/4.6 (A.A.P.) of the Ministry of Education and Science of the Russian Federation, by Project No. 15.61.202.2015 of Saint Petersburg State University (E.V.Ch.), and Grant No. IT-756-13 of the Basque Country University (E.V.Ch.).

Today, searching for materials hosting quantum anomalous Hall effect (QAHE) at high temperature and with long conductivity plateau is an important issue for next generation spintronic applications at nanoscale. In this article, we discuss a quantized spin Hall response in heterostructures composed of a three-dimensional topological insulator (TI) film and a ferromagnetic normal insulator (FMNI). The magnetic proximity effect at the TI/FMNI interface provides exchange splitting of the topological states in the TI film. We predict analytically that the FMNI/TI/FMNI trilayer can be driven into the QAHE state either from the topologically trivial state or the quantum spin Hall state, depending on the TI film thickness and the interface potential. We calculate the corresponding phase diagram of the FMNI/TI/FMNI trilayer. Our results provide a useful guide to realize the QAHE regime in the TI/FMNI heterostructures., This work was supported by the Grant No. 17-12-01345 of the Russian Science Foundation (in the part of analytic investigation of the electronic properties of FMNI/TI heterostructures). We also acknowledge the support from the Basque Country Government, Departamento de Educación, Universidades e Investigación (Grant No. IT-756-13), the Spanish Ministerio de Ciencia e Innovación (Grant No. FIS2016-75862-P) (in the part of calculation of anomalous Hall response), the Tomsk State University Academic D.I. Mendeleev Fund Program (Grant No. 8.1.05.2015), Saint Petersburg State University (Grant No. 15.61.202.2015) (in the part of numeric calculation of the phase diagram).

We report analytic investigation of the electronic properties of heterostructures comprised by films of three-dimensional topological insulator (TI) and normal insulator (NI) revealing strong interface and size effects on their spin transport characteristics. Imposing at the TI/NI interfaces the natural boundary conditions within a continual scheme, we show that the intrinsic spin Hall response of the NI/TI/NI trilayer can be controlled by tuning the interface potential (IP) together with the TI film thickness. We predict a series of interface induced quantum transitions between topological insulating phase and trivial band insulator phase. We calculate the phase diagram of the NI/TI/NI trilayer and establish an appropriate range of the IP strength and the TI film thickness to realize the regime of quantum spin Hall effect. Our results can provide a useful guide in choosing the relevant material parameters to facilitate the detection of quantum spin Hall conductivity in the TI/NI heterostructures., This work was supported by the Grant No. 17-19-01057 of the Russian Science Foundation (in the part of analytic investigation of the electronic properties of TI/NI heterostructures). We also acknowledge the support from the Basque Country Government, Departamento de Educación, Universidades e Investigación (Grant No. IT-756–13), the Spanish Ministerio de Ciencia e Innovación (Grant No. FIS2016-75862-P) (in the part of calculation of spin Hall response), the Tomsk State University Academic D.I. Mendeleev Fund Program (Grant No. 8.1.05.2015), Saint Petersburg State University (Grant No. 15.61.202.2015) (in the part of numeric calculation of the phase diagram).

Electron excitation spectra in Ti and Zr transition metals are calculated in the framework of time-dependent density functional theory. Several peaks found in the obtained loss functions are interpreted as collective excitations. The energy positions of the dominating bulk plasmons are in close agreement with the energy loss experiments. We investigated how the absorption of hydrogen modifies the dielectric properties of these materials. It is shown that the main plasmon energy blueshifts in a such process, again in agreement with experimental observations. On base of the calculated bulk dielectric functions of all these systems, we performed analysis of the excitation spectra at surfaces and nanoparticles. Several plasmon peaks in these systems with rather short lifetimes are found at reduced energies. It is shown how the nanoparticle excitation spectra are modified in the ultraviolet-frequency range upon hydrogen absorption., The research was funded by the Tomsk Polytechnic University Competitiveness Enhancement Program. I.V.S. acknowledges financial support from the Ministry of Education and Science of the Russian Federation within the governmental program Megagrants (State Task No. 3.9003.2017/220 or 3.9003.2017/9.10). V.M.S. and E.V.C. acknowledge the partial support from the University of the Basque Country UPV/EHU, Grant No. IT-756-13 and the Spanish Ministry of Economy, Industry and Competitiveness MINEICO, Project Nos. FIS2016-76617-P and FIS2016-75862-P. V.M.S. acknowledges project PI2017-30 of the Departamento de Educación, Política Lingüística y Cultura of the Basque government.

We present the density functional calculation results for K adsorption on Pt(111) in a (√3 × √3)R30° structure. The site preference, surface relaxation, work function, and electron structure of the system are analyzed. The hcp hollow position is found to be the most favorable for K adsorption. The calculated surface relaxations and adsorption geometry are in agreement with available experimental data. It is demonstrated that the K adsorption leads to the disappearance of a number of platinum surface and resonance states in the energy region above −2 eV and to the appearance of new platinum surface features, as well as bands that are significantly localized at the adsorbate. It is found that the K adsorption 1) transforms the Shockley surface state lying in the bulk band gap near the Γ¯ point on the clean Pt surface into the state localized at the K adlayer and 2) pushes this state up in energy by about 0.17 eV relative to the bottom of the bulk band gap. It is shown that the Rashba spin-orbit strength parameter in this state is surprisingly greater than the respective parameter in the Shockley surface state on Au(111) and Bi(111)., We acknowledge the Tomsk State University competitiveness programme (Project No. 8.1.01.2017) and partial support by the Saint Petersburg State University (Project No. 15.61.202.2015). Y.M.K. acknowledges the Russian Foundation for Basic Research (Project No. 15-02-02717-a) and the Fundamental Research Program of the State Academies of Sciences for 2013–2020. E.V.C. acknowledges the Spanish Ministry of Science and Innovation (Grant No. FIS2016-75862-P).

Strong spin-orbit coupling (SOC) in combination with a lack of inversion symmetry and exchange magnetic interaction proves to be a sophisticated instrument allowing efficient control of the spin orientation, energy and trajectories of two-dimensional (2D) electrons and holes trapped at surfaces or interfaces. Exploiting Kondo-related phenomena and crystal-electric-field effects at reduced dimensionalities opens new opportunities to handle their spin-dependent properties offering novel functionalities. We consider here a 2D Kondo lattice represented by a Si-Ir-Si-Yb (SISY) surface block of the heavy-fermion material YbIr2Si2. We show that the Kondo interaction with 4f moments allows finely tuning the group velocities of the strongly spin-polarized carriers in 2D itinerant states of this noncentrosymmetric system. To unveil the peculiarities of this interaction, we used angle-resolved photoemission measurements complemented by first-principles calculations. We established that the strong SOC of the Ir atoms induces spin polarization of the 2D states in SISY block, while the 2D lattice of Yb 4f moments acts as a source for coherent f−d interplay. The strong SOC and lack of inversion symmetry turn out to lead not only to the anticipated Rashba-like splitting of the 2D states, but also to spin splitting of the 4f Kramers doublets. They couple temperature-dependently to the spin-polarized 2D states and thereby guide the properties of the latter., This work was supported by the German Research Foundation (DFG; Grants No. GRK1621, No. KR3831/5-1, No. GE 602/4-1 Fermi Nest and No. SFB1143) as well as Research Grant No. 15.61.202.2015 of Saint-Petersburg State University. We also acknowledge the funding by the Basque Departamento de Educacion, UPV/EHU (Grant No. IT-756-13), the Spanish Ministry of Economy, Industry and Competitiveness MINEICO (Grants No. FIS2016-75862-P and No. FIS2016-76617-P), and Tomsk State University competitiveness improvement programme (project No. 8.1.01.2017)

We report a study of the interface between antimony and the prototypical topological insulator Bi2Se3. Scanning tunnelling microscopy measurements show the presence of ordered domains displaying a perfect lattice match with bismuth selenide. Density functional theory calculations of the most stable atomic configurations demonstrate that the ordered domains can be attributed to stacks of β-antimonene.

Detailed comparative theoretical and experimental study of electronic properties and spin structure was carried out for a series of Pb-based quaternary compounds ${\mathrm{PbBi}}_{2}{\mathrm{Te}}_{4\ensuremath{-}x}{\mathrm{Se}}_{x}$. For all values of $x$, these compounds are theoretically predicted to be topological insulators, possessing at high Se content a remarkably large band gap and a Dirac point isolated from bulk states. Using spin- and angle-resolved photoemission spectroscopy, it was shown that the ${\mathrm{PbBi}}_{2}{\mathrm{Te}}_{2}{\mathrm{Se}}_{2}$ and ${\mathrm{PbBi}}_{2}{\mathrm{Te}}_{1.4}{\mathrm{Se}}_{2.6}$ compounds are characterized by well-defined spin-polarized topological surface state in the bulk gap. To define the probable distribution of atoms over the atomic sites for these samples, we performed ab initio calculations in ordered and disordered configurations of the unit cell. We found that theoretical calculations better reproduce photoemission data when Te atoms are placed in the outermost layers of the septuple layer block.

We combine low energy muon spin rotation (LE-μSR) and soft-x-ray angle-resolved photoemission spectroscopy (SX-ARPES) to study the magnetic and electronic properties of magnetically doped topological insulators, (Bi,Sb)2Te3. We find that one achieves a full magnetic volume fraction in samples of (V/Cr)x(Bi,Sb)2-xTe3 at doping levels x=0.16. The observed magnetic transition is not sharp in temperature indicating a gradual magnetic ordering. We find that the evolution of magnetic ordering is consistent with formation of ferromagnetic islands which increase in number and/or volume with decreasing temperature. Resonant ARPES at the V L3 edge reveals a nondispersing impurity band close to the Fermi level as well as V weight integrated into the host band structure. Calculations within the coherent potential approximation of the V contribution to the spectral function confirm that this impurity band is caused by V in substitutional sites. The implications of our results on the observation of the quantum anomalous Hall effect at mK temperatures are discussed., The work at PSI was supported by the Swiss National Science Foundation (SNF-Grant No. 200021_165910). We acknowledge support from DFG through priority program SPP1666 (Topological Insulators), University of the Basque Country (Grants No. GIC07IT36607 and No. IT-756-13), Spanish Ministry of Science and Innovation (Grants No. FIS2013-48286-C02-02-P, No. FIS2013-48286-C02-01-P, and No. FIS2016-75862-P) and Tomsk State University competitiveness improvement programme (Project No. 8.1.01.2017). Partial support by the Saint Petersburg State University Project No. 15.61.202.2015 is also acknowledged. At MIT, C.Z.C. and J.S.M. acknowledge support from the STC Center for Integrated Quantum Materials under NSF grant DMR-1231319 as well as grants NSF (DMR-1207469, DMR1700137), ONR (N00014-13-1-0301 and N00014-16-1-2657). C.Z.C also acknowledges the support from the startup grant provided by Penn State University.

We study the effect of the Fermi surface anisotropy on the odd-frequency spin-triplet pairing component of the induced pair potential. We consider a superconductor/ ferromagnetic insulator (S/FI) hybrid structure formed on the 3D topological insulator (TI) surface. In this case three ingredients insure the possibility of the odd-frequency pairing: 1) the topological surface states, 2) the induced pair potential, and 3) the magnetic moment of a nearby ferromagnetic insulator. We take into account the strong anisotropy of the Dirac cone in topological insulators when the chemical potential lies well above the Dirac cone and its constant energy contour has a snowflake shape. Within this model, we propose that the S/FI boundary should be properly aligned with respect to the snowflake constant energy contour to have an odd-frequency symmetry of the corresponding pairing component and to insure the Majorana bound state at the S/FI boundary. For arbitrary orientation of the boundary the Majorana bound state is absent. This provides a selection rule to the realization of Majorana modes in S/FI hybrid structures, formed on the topological insulator surface., 7 pages, 2 figures

A theoretical study of collective electronic excitations in free-standing Pb(111) thin films consisting of 1-5 monolayers (MLs) and a 21-ML film is presented. The calculations are carried out applying the linear response theory, with full inclusion of the electron band structure by means of a first-principles pseudopotential approach in a supercell scheme. In the case of the thickest film, we find that, due to strong bulklike interband transitions, at the Pb(111) surface there are two surface modes. For thin films, a mechanism of transformation of these modes to the symmetric and antisymmetric classic hybrid plasmons is investigated. Pronounced quantum-size effects on plasmon modes of the thinnest films are found. Strong influence of the band structure on dispersion and lifetime of such modes is demonstrated. The present results are in good agreement with available experimental data for a Pb surface and thin films., E.V.C. and V.M.S. acknowledge the partial support from the University of the Basque Country UPV/EHU, Grant No. IT-756-13, and the Spanish Ministry of Economy and Competitiveness MINECO, Grant No. FIS2016-76617-P.

Using surface x-ray diffraction and scanning tunneling microscopy in combination with first-principles calculations, we have studied the geometric and electronic structure of Cs-deposited ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$(0001) surface kept at room temperature. Two samples were investigated: a single ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ crystal, whose surface was Ar sputtered and then annealed at $\ensuremath{\sim}500{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ for several minutes prior to Cs deposition, and a 13-nm-thick epitaxial ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ film that was not subject to sputtering and was annealed only at $\ensuremath{\sim}350{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$. In the first case, a considerable fraction of Cs atoms occupy top layer Se atoms sites both on the terraces and along the upper step edges where they form one-dimensional-like structures parallel to the step. In the second case, Cs atoms occupy the $fcc$ hollow site positions. First-principles calculations reveal that Cs atoms prefer to occupy Se positions on the ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$(0001) surface only if vacancies are present, which might be created during the crystal growth or during the surface preparation process. Otherwise, Cs atoms prefer to be located in $fcc$ hollow sites in agreement with the experimental finding for the MBE-grown sample.

Momentum-resolved photoemission spectroscopy indicates the instability of the Dirac surface state upon deposition of gold on the (0001) surface of the topological insulator Bi2Se3. Based on the str ...

In this work, we employed angle resolved photoemission spectroscopy (ARPES) to analyze the temperature dependent changes in the electronic structure of the first antiferromagnetic topological insulator MnBi2Te4 upon crossing the Néel temperature TN ≈ 25 K. We observed an exchange splitting of the bulk conduction band, which has a power law dependence on temperature (1−T/T0)2β with an onset temperature T0 well matching the measured bulk TN. We found a matching temperature evolution of the topological surface states integrated spectral weight in the vicinity of the Dirac point. Furthermore, we observed an additional quasi-2D state with Rashba-type splitting, which is also affected by the emerged magnetism and exhibits an opening of a gap, reminiscent of the effect of an out-of-plane magnetic field, below TN. All these findings point toward strong evidence of the interplay between emerged magnetism with bulk and topological surface states. The observed temperature-dependent effects in MnBi2Te4 may be used as an experimental fingerprint for the presence of magnetism and may guide the future analysis of ARPES spectra in magnetic topological insulators., The authors acknowledge support from the Saint Petersburg State University (Grant No. 51126047), the Russian Science Foundation (Grant No. 18-12-00062), and the Russian Foundation for Fundamental Investigations (No. 20-32-70179). The ARPES experiments were performed at HiSOR under Proposal Nos. 18BG026 and 18BU006. A. Kimura was financially supported by KAKENHI (Grant Nos. 17H06138, 17H06152, and 18H03683). Z. S. Aliev and M. B. Babanly acknowledge support from the Science Development Foundation under the President of the Republic of Azerbaijan (Grant No. EIF/MQM/Elm-Tehsil-1-2016-1(26)-71/01/4-M-33). The support by Tomsk State University competitiveness improvement program (No. 8.1.01.2018) is gratefully acknowledged.

The atomic and phonon structures of a Pb ultrathin film on the Al(100) surface have been theoretically studied. Surface relaxation, local density of vibrational states, and polarization of the phonon modes of adatoms and atoms of a substrate have been discussed. It has been shown that the adsorption of Pb results in the oscillating relaxation of the surface of the substrate and warping of the structure in subsurface layers. Comparative analysis of the vibrational characteristics of the pure surface of the substrate and the surface with adatoms has shown that the adsorptive interaction in the system and its dynamic stability are governed by new vibrational modes that are not inherent in pure Al and Pb surfaces., This work was supported by the Government of the Russian Federation (Program of Basic Research at State Academies of Sciences for 2013–2020). The numerical calculations were performed at the SKIF Cyberia supercomputer (Tomsk University).

The topological insulators Bi2Se3 and Bi2Te2Se have been shown to possess unoccupied topological surface states at the center of the surface Brillouin zone at energies around 1.3 eV above the Fermi level. Using time-resolved two-photon photoemission we study the electron dynamics of the unoccupied topological surface states, image-potential states and conduction bands on these surfaces., The present work was partially supported by RFBR (Grant Nos. 12-02-00226 and 13-02-12110).

Recently, it was shown that quantum spin Hall insulator phase with a gap wide enough for practical applications can be realized in the ultrathin films constructed from two inversely stacked structural elements of trivial band insulator BiTeI. Here, we study the edge states in nanoribbons made of the Bi2Te2I2 sextuple layer (SL) and the electronic structure of the SL deposited on the natural BiTeI substrate as well as sandwiched between two thick BiTeI films. We show that the Bi2Te2I2 SL keeps nontrivial topological properties. We also demonstrate that ultrathin centrosymmetric films constructed in a similar manner from related material BiTeBr are trivial band insulators up to five-SL film thickness. In contrast to Bi2Te2I for which the stacking of nontrivial SLs in a three-dimensional (3D) limit results in a strong topological insulator (TI) phase, a 3D TI Bi2Te2Br2 is formed by trivial SLs. For the last material of the BiTeX (X=I,Br,Cl) series, BiTeCl, both 2D and 3D centrosymmetric phases are characterized by topologically trivial band structure., This work was supported by the Spanish Ministry of Economy and Competitiveness MINECO (Project No. FIS2016-76617-P), Saint Petersburg State University (Grant No. 15.61.202.2015), Tomsk State University competitiveness improvement programme (Project No. 8.1.01.2017), and RFBR (Grant No. 15-02-02717-a).

The theoretical studies of phase states with a linear dispersion of the spectrum of low-energy electron excitations have been reviewed. Some main properties and methods of experimental study of these states in socalled Dirac materials have been discussed in detail. The results of modern studies of symmetry-protected electronic states with nontrivial topology have been reported. Combination of approaches based on geometry with homotopic topology methods and results of condensed matter physics makes it possible to clarify new features of topological insulators, as well as Dirac and Weyl semimetals., The work of E.V.Ch. was supported in part by the San Sebastian University (grant no. IT-756-13).

Two-and three-dimensional topological insulators are the key materials for the future nanoelectronic and spintronic devices and quantum computers. By means of angle-and spin-resolved photoemission spectroscopy we study the electronic and spin structure of the Bi-bilayer/3D topological insulator in quantum tunneling regime formed under the short annealing of BiTeSe Owing to the temperature-induced restructuring of the topological insulator's surface quintuple layers, the hole-like spin-split Bi-bilayer bands and the parabolic electronic-like state are observed instead of the Dirac cone. Scanning Tunneling Microscopy and X-ray Photoemission Spectroscopy measurements reveal the appearance of the Bi terraces at the surface under the annealing. The experimental results are supported by density functional theory calculations, predicting the spin-polarized Bi-bilayer bands interacting with the quintuple-layers-derived states. Such an easily formed heterostructure promises exciting applications in spin transport devices and low-energy electronics., The work was partially supported by grant of Saint Petersburg State University for scientific investigations (No 15.61.202.2015). We acknowledge the financial support of the University of Basque Country UPV/EHU (Grant No. GIC07-IT-756-13), the Departamento de Educación del Gobierno Vasco and the Spanish Ministerio de Ciencia e Innovación (Grant No. FIS2010-19609-C02-01), the Spanish Ministry of Economy and Competitiveness MINECO (Grant No. FIS2013-48286-C2-1-P) and the Tomsk State University Competitiveness Improvement Program.

We present first-principles calculations of electronic structure and topological properties of thin films of tetradymite-like binary, ternary, and quaternary compounds. Two-dimensional topological insulators were found, including two septuple layer films of PbBi2Te4 with large band gap. We demonstrate that the Pb-based thin films inherit Z2 dependence on the film thickness from the >parent> quintuple-layer compounds. An effective way to induce the topological phase transition in the trivial thin films is proposed that does not require substantial changes in the in-plane lattice parameter and surface crystal structure., This paper is supported by Tomsk State University competitiveness improvement programme (Project No. 8.1.01.2017), the Saint Petersburg State University Project No. 15.61.202.2015, the Ministry of Education and Science of the Russian Federation within the framework of the governmental program Megagrants (State Task No. 3.8716.2017/220 or 3.8716.2017/9.10), the University of the Basque Country (Grants No. GIC07IT36607 and No. IT-756-13), the Spanish Ministry of Science and Innovation (Grants No. FIS2013-48286-C02-02-P, No. FIS2013-48286-C02-01-P, and No. FIS2016-75862-P).