Guaranteed Solution and its Finding in the Integer Programming Problems

Abstract In the work the definitions of the guaranteed solution and guaranteed suboptimal solution are given for the multiconstraint integer programming problem. A method is developed for finding these solitions. This method is based on the sequental changing of the right hand side of the system of constraints by the dichotomia ous principle

Temperature studies of Raman spectra in MnBi2Te4 and MnSb2Te4 magnetic topological insulators

Raman spectra of magnetic topological crystalline insulators in a wide temperature range including the magnetic ordering region are studied in detail. The anharmonicity parameters and Grüneisen mode parameters of Raman-active phonons in the studied crystals have been determined. It has been shown that the temperature dependence of the frequency of the (~48 cm–1) phonon in MnBi2Te4 coincides within ±0.1 cm–1 with the standard anharmonic model disregarding the spin–phonon coupling. The polarization dependences of Raman spectra in the MnSb2Te4 crystals indicate that Sb and Mn atoms are strongly mixed in them unlike the isostructural MnBi2Te4 crystals.This work was supported by the Azerbaijan Ministry of Science and Education (program “Development of the Preparation Technology of Multifunctional Convertors Based on Nanostructures”). E.V.C. acknowledges the s-upport of St. Petersburg State University (project no. 94031444).Peer reviewe

The charge transport mechanism in a new magnetic topological insulator MnBi0.5Sb1.5Te4

A new layered magnetic topological insulator with the composition MnBi0.5Sb1.5Te4 is obtained. The electrical conductivity in the plane of the layers and in the direction normal to the layers is studied in the range of temperatures of 1.4–300 K. It is found that a “metallic” character of the temperature dependence of the resistivity ρ(T) is observed in the range of temperatures of 50–300 K in both directions. Below T = 50 K, the value of ρ increases and demonstrates an uncommon temperature dependence with a characteristic feature in the region of the critical temperature Tc = 23 K. The increase in the resistance in the temperature range of 50–23 K is determined by the spin fluctuations and magnetic phase transition. Below Tc and down to 1.4 K, ρ(T) demonstrates a behavior characteristic for the weak localization effect, which is confirmed by the analysis of the data obtained when studying magnetoresistance.This work was financially supported by the Science Development Foundation under the President of the Republic of Azerbaijan (grants nos. EİF-BGM-4-RFTF-1/2017-21/04/1-M-02, EİF/MQM/Elm-Tehsil-1-2016-1(26)-71/16/1), Russian Foundation for Basic Research (grant no. 18-52-06009), St. Petersburg State University (grant no. 73028629) as well as the Spanish Ministerio de Ciencia e Innovación Foundation (grant no. PID2019-103910GB-I00).Peer reviewe

Transport properties of the magnetic topological insulators family (MnBi2Te4)(Bi2Te3)m (m = 0, 1, …,6)

Systematic studies of magneto-transport properties of the whole (MnBi2Te4)(Bi2Te3)m family of magnetic topological insulators ( have been carried out. Temperature dependences of the resistivity, magnetoresistance and the Hall effect at low temperatures have been studied. When m increases, i.e., when the separation between 2D MnBi2Te4 magnetic layers becomes larger, the transition from antiferromagnetic to ferromagnetic state takes place. We have found that ferromagnetic state survives even in the samples with, when 2D magnets are separated by six non-magnetic Bi2Te3 blocks.N.T. Mamedov acknowledges the support of the Azerbaijan Ministry of Science and Education (research program “Development of the Preparation Technology of Multifunctional Convertors Based on Nanostructures”). E.V. Chulkov acknowledges the support of the St. Petersburg State University, (project ID no. 94031444).Peer reviewe

Lattice dynamics of Bi2Те3 and vibrational modes in Raman scattering of topological insulators MnBi2Te4·n(Bi2Te3)

This work is devoted to the experimental study and symmetry analysis of the Raman-active vibration modes in MnBi2Te4 center dot n(Bi2Te3) van der Waals topological insulators, where n is the number of Te-Bi-Te-Bi-Te quintuple layers between two neighboring Te-Bi-Te-Mn-Te-Bi-Te septuple layers. Confocal Raman spectroscopy is applied to study Raman spectra of crystal structures with n = 0,1, 2, 3, 4, 5, 6, and infinity. The experimental frequencies of vibration modes of the same symmetry in the structures with different n are compared. The lattice dynamics of free-standing one, three, and four quintuple layers, as well as of bulk Bi2Te3 (n = infinity) and MnBi2Te4 (n = 0), is considered theoretically. Vibrational modes of the last two systems have the same symmetry, but different displacement fields. These fields in the case of a Raman-active mode do not contain displacements of manganese atoms for any finite n. It is shown that two vibrational modes in the low-frequency region of the spectrum (35-70 cm(-1)) of structures with n = 1, 2, 3, 4, 5, and 6 practically correspond to the lattice dynamics of n free quintuple Bi2Te3 layers. For this reason, the remaining two vibration modes, which are observed in the high-frequency region of the spectrum (100-140 cm(-1)) and are experimentally indistinguishable in the sense of belonging to quintuple or septuple layer or to both layers simultaneously, should also be assigned to vibrations in quintuple layers under immobile atoms of septuple layers

Crystal structure and Raman-active lattice vibrations of magnetic topological insulators MnBi2Te4·n(Bi2Te3) (n=0, 1,⋯,6)

Further to the structure of the intrinsic magnetic topological insulators MnBi2Te4⋅n(Bi2Te3) with n0 overwhelmingly dominates by the cooperative atomic displacements in the quintuple building blocks.This work was performed within the research program “Development of preparation technology of multifunctional convertors based on nanosized structures” and was supported by TÜBITAK- ANAS Project No. 120N296. M.M.O. acknowledges the support by Spanish Ministerio de Ciencia e Innovación (Grant No. PID2019-103910GB-100). E.V.C. acknowledges support from Saint Petersburg State University (Project ID No. 90383050).Peer reviewe

Novel ternary layered manganese bismuth tellurides of the MnTe-Bi2Te3 system: Synthesis and crystal structure

It is shown that MnTe-Bi2Te3 system is quasi-binary and in fact hosts three intermediate phases. Along with already known MnBi2Te4 phase, another two, MnBi4Te7 and MnBi6Te10 have been found to exist. All the phases melt incongruently in a very narrow temperature range of 577–590 °C via peritectic reactions. Directional crystal growth results in hetero-phase ingots due to the narrow compositional range and narrow primary crystallization fields. The crystal structure of each phase is a derivation of the prototype tetradymit-type layered structure and the phases constitute a new homologous series with the chemical formula (MnTe)·n(Bi2Te3). X-ray diffraction patterns and Raman spectroscopy of the sorted-out single phase samples show that different phases have different number of the seven (7)- and five (5)-layer blocks and their different stacking manner in the unit cell. In particular, MnBi2Te4 exhibits the -7-7-7-, MnBi4Te7 -5-7-5-7-, and MnBi6Te10 -5-5-7-5-5-7- sequence of the blocks. Thus, these structures are the first derivatives of Bi2Te3 structure to contain a transition metal cation Mn2+

Electronic structure and dielectric function of Mn-Bi-Te layered compounds

A comparative study of the electronic and optical properties of Mn-Bi-Te layered compounds was carried out using spectroscopic ellipsometry (SE) over a photon energy range of 0.7-6.5 eV at room temperature and density functional theory (DFT)-based first-principle calculations within the general gradient approximation with Hubbard like correction (GGA+U) and allowance for a spin-orbital coupling. The total energies of the above compounds in ferromagnetic (FM) and antiferromagnetic (AFM) spin configurations are obtained by taking the long-range van der Waals interaction into account. The stability of the AFM state of MnBiTe and MnBiTe over the corresponding FM counterpart is disclosed. The SE-based and calculated dielectric functions are compared. It is shown that interband optical transitions in the accessed photon energy range mainly occur between Mn 3d + Te 5p states of the valence band and Bi 6p + Te 5p with a small admixture of Mn 3d states of the conduction band.We acknowledge the support by the Science Development Foundation under the President of the Republic of Azerbaijan (Grant No. EI F-BGM-4-RFTF1/2017-21/04/1-M-02), Russian Foundation for Basic Research (Grant No. 18-52-06009), the Basque Departamento de Educación, UPV/EHU (Grant No. IT-756-13), Spanish Ministerio de Economia y Competitividad (MINECO Grant No. FIS2016-75862-P), the Saint Petersburg State University grant for scientific investigations (Grant No.15.61.202.2015). M.M.O. acknowledges support by the Diputación Foral de Gipuzkoa (SAREA 2018 - RED 2018*, *Project No. 2018-CIEN-000025-01)

Infrared spectroscopic ellipsometry and optical spectroscopy of plasmons in classic 3D topological insulators

Narrow bandgap BiSe, BiTe, and SbTe, commonly referred to as classic 3D topological insulators, were studied at room temperature by spectroscopic ellipsometry and optical reflection spectroscopy over the mid-IR-near-infrared photon energy range. Complementarily, Hall measurements were performed. Plasmons in optical loss function and reflection coefficient were identified. The conventional approach based on the high frequency dielectric constant was shown to work well in the description of plasmons in BiSe and SbTe and to fail in the case of a similar compound, BiTe. The obtained results are discussed in terms of single- and multivalley approaches to the studied samples with taking the details of the calculated band structure into account.This work was supported by the Science Development Foundation under the President of the Republic of Azerbaijan (Grant No. EI F-BGM-4-RFTF1/2017-21/04/1-M-02 and EİF-BGM-3-BRFTF-2+/2017-15/02/1), the Russian Foundation for Basic Research (Grant No. 18-52-06009), and the Saint Petersburg State University grant for scientific investigations (Grant No. 15.61.202.2015)