Effect of the atomic composition of the surface on the electron surface states in topological insulators A<Stack><Subscript>2</Subscript><Superscript>V</Superscript></Stack>B<Stack><Subscript>3</Subscript><Superscript>VI</Superscript></Stack>

The results of the theoretical investigation of the surface electronic structure of A₂^VB₃^VI compounds containing topologically protected surface states are reported. The ideal Bi₂Te₃, Bi₂Se₃, and Sb₂Te₃ surfaces and surfaces with an absent external layer of chalcogen atoms, which were observed experimentally as monolayer terraces, have been considered. It has been shown that the discrepancy between the calculated Fermi level and the value measured in the photoemission experiments can be attributed to the presence of the “dangling bond” states on the surface of the terraces formed by semimetal atoms. The fraction of such terraces on the surface has been estimated.     

Bond ionicity and susceptibility in aIbIIIc2VI compounds

The electronic susceptibilities, energy gaps and the bond ionicities of some A^IB^IIIC₂^VI chal-copyrite compounds have been calculated from their plasmon energy. The effect of delocalization of noble metal d-electrons has been taken into account while calculating these parameters in the case of the A^I-C^VI bond. A comparison is made between the present results and the results of previous calculations.     

Raman scattering study of pressure-induced phase transitions in AIIB2IIIC4VI defect chalcopyrites and spinels

A^IIB₂^IIIC₄^VI defect chalcopyrites (DC) and spinels were investigated by Raman scattering spectroscopy under hydrostatic pressure up to 20 GPa. All these compounds were found to undergo a phase transition to a Raman inactive defect NaCl-type structure. The phase transition is reversible for spinels and irreversible for DC. From the analysis of the pressure behavior of Raman-active modes, it was concluded that the phase transition from spinel to NaCl-type structure is direct in MnIn₂S₄ and CdIn₂S₄, while it occurs via an intermediate LiVO₂-type NaCl superstructure in MgIn₂S₄. The observed differences in the pressures and the paths of the pressure-induced phase transitions in A^IIB₂^IIIC₄^VI compounds are discussed.     

Atomic chains and lattice vibration characteristics in A2 IIIB3 VI compounds with tetrahedral coordination of atoms

On the basis of the presence of atomic chains in A₂ ^IIIB₃ ^VI compounds having zincblende defect structure, a linear-chain model is used to calculate the lattice vibration frequencies. The agreement of the calculated and experimental frequencies is an indication of the applicability of the model and enables one to determine the motion of various atoms during the corresponding vibrations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 83–88, April, 1977.     

Three- and two-dimensional topological insulators in Pb2Sb2Te5, Pb2Bi2Te5, and Pb2Bi2Se5 layered compounds

The electronic structure of ternary compounds Pb₂Sb₂Te₅, Pb₂Bi₂Te₅, and Pb₂Bi₂Se₅, which have a layered structure that consists of nine-layer atomic blocks separated by van der Waals gaps, has been theoretically studied. It has been shown that all studied compounds are three-dimensional topological insulators. The possibility of the existence of a two-dimensional topological insulator has been found in ultrathin (0001) Pb₂Sb₂Te₅ and Pb₂Bi₂Te₅ films. Oscillations of the ℤ₂ topological invariant with an increase in the film thickness have been observed in the latter compound.     

Thermal property of binary tetrahedral semiconductors

In this paper we present an expression relating the lattice thermal expansion coefficient α_L (10⁻⁶ K⁻¹) for the A^IIIB^V and A^IIB^VI semiconductors with the product of ionic charges (Z₁Z₂), melting temperature (T_m) and nearest neighbor distance d (Å). The lattice thermal expansion coefficient of these compounds exhibit a linear relationship when plotted on a log–log scale against the melting temperature (T_m), but fall on different straight lines according to the ionic charge product of the compounds. A good agreement has been found between the experimental and calculated values of the lattice thermal expansion coefficient for A^IIIB^V and A^IIB^VI semiconductors.     

On the origin of two-dimensional electron gas states at the surface of topological insulators

The ab initio calculations of the electronic structure in the bulk and at the (0001) surface of narrow-band Bi₂Se₃, Sb₂Te₃, Sb₂STe₃, and Sb₂SeTe₂ semiconductors have been performed. It has been shown that ternary compounds Sb₂STe₂ and Sb₂SeTe₂, as well as the previously known compounds Bi₂Se₃ and Sb₂Te₃, are three-dimensional topological insulators. The influence of the subsurface van der Waals gap expansion on the surface electronic structure of these compounds has been analyzed. It has been shown that this expansion leads to the formation of new (trivial) surface states, namely a parabolic state in the conduction band and an M-shaped state in the valence band. These results explain the phenomena discovered recently in photoemission experiments and reveal the nature of new states that are caused by the adsorption of atoms on the surfaces of the layered topological insulators.     

Internal energy of AB2X4 crystalline compounds. Electrostatic energy contribution for compounds with closed shell cations

Madelung energy calculations are performed for two different lattices in which some of AB₂X₄ compounds (A = M⁺², B = M^?3, X = O^?2, S^?2, Se^?2, Te^?2) crystalline.A gross evaluation of the covalent bond energy contribution in the same crystals is made and some considerations are draw from the comparison between the two above quoted energy contributions.     

Specific features of the electronic,spin, and atomic structures of a topological insulator Bi<Subscript>2</Subscript>Te<Subscript>2.4</Subscript>Se<Subscript>0.6</Subscript>

The specific features of the electronic and spin structures of a triple topological insulator Bi₂Te_2.4Se_0.6, which is characterized by high-efficiency thermoelectric properties, have been studied with the use of angular- and spin-resolved photoelectron spectroscopy and compared with theoretical calculations in the framework of the density functional theory. It has been shown that the Fermi level for Bi₂Te_2.4Se_0.6 falls outside the band gap and traverses the topological surface state (the Dirac cone). Theoretical calculations of the electronic structure of the surface have demonstrated that the character of distribution of Se atoms on the Te–Se sublattice practically does not influence the dispersion of the surface topological electronic state. The spin structure of this state is characterized by helical spin polarization. Analysis of the Bi₂Te_2.4Se_0.6 surface by scanning tunnel microscopy has revealed atomic smoothness of the surface of a sample cleaved in an ultrahigh vacuum, with a lattice constant of ~4.23 Å. Stability of the Dirac cone of the Bi₂Te_2.4Se_0.6 compound to deposition of a Pt monolayer on the surface is shown.     

Magnetic susceptibility of multinary diamondlike semiconductors

Summary The magnetic susceptibility of some A^IB ₂ ^II C^IIIX ₄ ^VI (A^I=Cu, Ag; B^II=Zn, Cd; C^III=Ga, In; X^VI=Se, Te) diamondlike chalcogenides has been measured at RT. Coherently with the form of the relative A^IC^IIIX ₂ ^VI -B^IIX^VI phase diagrams, their magnetic susceptibility fulfils the sum rule typical of ideal solid solutions. Separate values of the diamagnetic and paramagnetic contributions to total magnetic susceptibility are reported and discussed according to a chemical-bond approach previously described. Paper presented at the ?V International Conference on Ternary and Multinary Compounds?, held in Cagliari, September 14–16, 1982.     

Magnetic properties of stuffed copper chromium tellurides Cu1+xCr2+yTe4 (x=0-1, y<0.3)

We present a detail study of the effect of excess metal atoms on the magnetic properties of Cu_1+xCr_2+yTe₄ at 2-400 K. With the increase in x=0-1 and y<0.3, these compounds retain metallic behavior, while ferromagnetic ordering temperature reduces from 325 to 160 K. Our low field susceptibility χ_ac measurements reveal a second transition on cooling below the ferromagnetic ordering; the transition at around 160-180 K intensifies with the excess amount of copper and chromium atoms. The value of spontaneous magnetization at 2 K remains between 2.6 and 2.9μ_B across all the compositions and it reduces with temperature as M(T)∼A₀T^3/2+A₁T^5/2, as expected for the excitation of Bloch's spin waves in a model of the Heisenberg ferromagnet. Our terminal composition Cu_1.9Cr_2.25Te₄ showed only second transition at 160 K with short range magnetic order much above the transition temperature and in the absence of the specific heat jump at this temperature. The magnetic properties are explained as a result of random magnetic anisotropy in the excess-metal compositions induced by the interstitial atomic defects in their parent spinel structure. The large stuffing of cations has been made possible in the telluride compounds because of the large size of tellurium and also by the covalent bonding that stabilizes the defect structure.     

Cohesive energy of zincblende (A<Superscript>III</Superscript>B<Superscript>V</Superscript> and A<Superscript>II</Superscript>B<Superscript>VI</Superscript>) structured solids

In this paper we present an expression relating the cohesive energy (E _coh in kcal/mol) of A^IIIB^V and A^IIB^VI semiconductors with the product of ionic charges (Z ₁ Z ₂) and nearest-neighbour distance d (Å). The cohesive energy values of these solids exhibit a linear relationship when plotted on a log-log scale against the nearest-neighbour distance d (Å), but fall on different straight lines according to the ionic charge product of the solids. A good agreement has been found between the experimental and calculated values of the cohesive energy of A^IIIB^V and A^IIB^VI semiconductors.     

On kinetic phenomena in semiconducting compounds of AIBIIIC2 VI type with chalcopyrite lattice

A four-ellipsoid model of the vertex of the valence band, proposed earlier for some semiconducting compounds of type A^IB^IIIC₂ ^VI, is examined. The anisotropy of the galvano- and thermomagnetic effects is studied under the assumption of an anisotropic relaxation time and the presence of one scattering mechanism.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–51, July, 1973.     

Energy band structure and modulation spectra of A2B4C25 semiconductors

The results of the energy band structure calculations of A²B⁴C₂⁵ compounds are reviewed, and the differences in the energy spectra passing from A³B⁵ semiconductors to their closest ternary analogs are described. The origin of the lowest conduction band minima of A²B⁴C₂⁵ compounds was determined from the slopes of the fundamental absorption edge and the pressure coefficients of the energy gap. The investigations of the valence band structure from electroreflectance (ER), thermoreflectance (TR) and wavelength modulated absorption (WMA) spectra are reviewed. In the higher energy region the ER and TR spectra of A²B⁴C₂⁵ compounds were found to be more complicated in comparison with those of their binary analogs. A model of an assignment of the structures in optical spectra of A²B⁴C₂⁵ compounds is discussed.     

Phase stability and electronic structure of Si2Sb2Te5 phase-change material

On the basis of an ab initio computational study, the present work provide a full understanding on the atomic arrangements, phase stability as well as electronic structure of Si₂Sb₂Te₅, a newly synthesized phase-change material. The results show that Si₂Sb₂Te₅ tends to decompose into Si₁Sb₂Te₄ or Si₁Sb₄Te₇ or Sb₂Te₃, therefore, a nano-composite containing Si₁Sb₂Te₄, Si₁Sb₄Te₇ and Sb₂Te₃ may be self-generated from Si₂Sb₂Te₅. Hence Si₂Sb₂Te₅ based nano-composite is the real structure when Si₂Sb₂Te₅ is used in electronic memory applications. The present results agree well with the recent experimental work.     

Tetragonal distortion for AIBIIICVI2 chalcopyrite compounds

Pauli-force constants and Simons-Bloch radii for the atoms of groups IB, III and VI are reported. The latter have been used to define a dimensionless quantity ΔX_ch which is found to be correlated in an analytical way with the observed tetragonal distortion δ of A^IB^IIIC^VI₂ type chalcopyrite compounds.     

Bond-stretching and bond-bending force constant of binary tetrahedral (AB and AB) semiconductors

In this Letter we present the two expressions relating the bond-stretching force constant (α in N/m) and bond-bending force constant (β in N/m) for the A^IIIB^V and A^IIB^VI semiconductors with the product of ionic charges (Z₁Z₂) and nearest neighbor distance d (Å). Interatomic force constants of these compounds exhibit a linear relationship when plotted on a log-log scale against the nearest neighbor distance d (Å), but fall on different straight lines according to the ionic charge product of the compounds. A fairly good agreement has been found between the observed and calculated values of the α and β for binary tetrahedral semiconductors.     

The Growth of P-type TlGaSe2(1−x) S2x Single Crystals

TlGaSe_2(1–x) S_2x single crystals were grown by the modified Bridgman-Stockbarger method in our crystal growth laboratory. A^IIIB^III C₂ ^VI compounds are formed of elements from vertical groups of the periodic table (group III: Tl, Ga, In; group VI: Se, S, Te) and are classified into two types. The first type has a layer structure: TlGaSe₂, TlGaS₂ and TlInS₂. The second type has a chained structure: TlInSe₂, TlInTe₂ and TlGaTe₂. None of the grown crystals had cracks and voids on the surface. The freshly cleaved crystals had a mirror-like surface and there was no need for mechanical or chemical polishing treatments. By the hot probe technique, we have found that the crystals were of p-type. The ingots produced were single crystalline and the useful region of single crystal was 90% with steps of 10 K if changes were small, and with steps of 3 and 5 K if changes were large in the direct and indirect band gaps energies. The direct and indirect band gaps for TlGaSe_2(1–x)S_2x samples were calculated as a function of temperature.     

Ab initio calculations of neutral and charged impurity centers of manganese and chromium in strontium titanate

This paper presents the results of ab initio calculations of the equilibrium geometry, the electronic structure, and the spin and charge densities for neutral and negatively charged defects produced by the Mn and Cr impurities in the B position of the SrTiO₃ structure. It has been shown that, in both cases, the neutral defect is an acceptor center, while the singly charged defect is a donor center. It has been found that doubly charged defects are polar, have the symmetry C _4v, and reside in the ionic configurations ⁵Mn³⁺ + ³Ti³⁺ and ⁴Cr³⁺ + ³Ti³⁺, respectively. In each case, there is a pair of almost energy-degenerate electronic states (⁴ B ₁ and ⁶ B ₁ for Mn and ³ A ₁ and ⁵ A ₁ for Cr), which differ only in the direction of the spin of the electron polaron localized at one of the neighboring titanium atoms. For the manganese impurity, the energy of the polar state ⁶ B ₁ is only 0.174 eV lower than that of the state ⁶ A _1g (O _h ) with the Mn²⁺ ion in the high-spin state. A new mechanism of dielectric relaxation in STO: Mn has been proposed.