Energy band structure and X-ray spectra of phenakite Be<Subscript>2</Subscript>SiO<Subscript>4</Subscript>

The electronic structure of crystalline phenakite Be₂SiO₄ is investigated using x-ray emission spectroscopy (XES) (Be K _α XES, Si L _{2, 3} XES, O K _α XES) and x-ray absorption spectroscopy (XAS) (Be 1s XAS, Si 2p XAS, O 1s XAS). The energy band structure is calculated by the ab initio full-potential linearized augmented-plane-wave (FLAPW) method. The total and partial densities of states and the dispersion curves for the Be₂SiO₄ compound are presented. It is shown that the top of the valence band and the bottom of the conduction band of the Be₂SiO₄ compound are predominantly formed by the oxygen 2p states. According to the results obtained, the electron transition with the lowest energy supposedly can occur at the center of the Brillouin zone. The effective masses of electrons (0.5m _e ) and holes (3.0m _e ) for the Be₂SiO₄) compound are estimated.     

Electronic structure of α-Al<Subscript>2</Subscript>O<Subscript>3</Subscript>: Ab initio simulations and comparison with experiment

Al₂O₃ films 150 Å thick are deposited on silicon by the ALD technique, and their x-ray (XPS) and ultraviolet (UPS) photoelectron spectra of the valence band are investigated. The electronic band structure of corundum (α-Al₂O₃) is calculated by the ab initio density functional method and compared with experimental results. The α-Al₂O₃ valence band consists of two subbands separated with an ionic gap. The lower band is mainly formed by oxygen 2s states. The upper band is formed by oxygen 2p states with a contribution of aluminum 3s and 3p states. A strong anisotropy of the effective mass is observed for holes: m _h⊥ ^* ≈ 6.3m ₀ and m _h‖ ^* ≈ 0.36m ₀. The effective electron mass is independent of the direction m _e‖ ^* ≈ m _e⊥ ^* ≈ 0.4m ₀.     

Energy spectrum of holes in Sb<Subscript>2</Subscript>Te<Subscript>2.9</Subscript>Se<Subscript>0.1</Subscript> solid solution according to the data on the transfer phenomena

The temperature dependence of the Hall coefficient of a single crystal of the p-Sb₂Te_2.9Se_0.1 solid solution grown by the Czochralski technique is studied in the temperature range 77–450 K. The data on the Hall coefficient of the p-Sb₂Te_2.9Se_0.1 are analyzed in combination with the data on the Seebeck and Nernst–Ettingshausen effects and the electrical conductivity with allowance for interband scattering. From an analysis of the temperature dependences of the four kinetic coefficients, it follows that, at T < 200 K, the experimental data are qualitatively and quantitatively described in terms of the one-band model. At higher temperatures, a complex structure of the valence band and the participation of the second-kind additional carriers (heavy holes) in the kinetic phenomena should be taken into account. It is shown that the calculations of the temperature dependences of the Seebeck and Hall coefficients performed in the two-band model agree with the experimental data with inclusion of the interband scattering when using the following parameters: effective masses of the density of states of light holes m_d1^*≈ 0.5m₀ (m₀ is the free electron mass) and heavy holes m_d2^*≈ 1.4m₀, the energy gap between the main and the additional extremes of the valence band ΔE_v ≈ 0.14 eV that is weakly dependent on temperature.     

Dependence of the upper critical field on the defect concentration in MgB<Subscript>2</Subscript> and the electronic structure parameters

The upper critical field H _c 2 (H ‖ c) of the two-band superconductor MgB₂ is studied as a function of the residual resistivity ρ_n. It is found that the superconductor follows the standard trend: the slope-dH_c2/dT of the temperature dependence of H_c2(T) increases with the number of defects. The upper critical field in the clean limit is found, and direct estimations of the parameters of carriers in the 2D σ band (including the Fermi velocity and the coherence length) are made. The contribution of the electron scattering to the magnitude of H_c2 is determined, and the mean free path of electrons in samples with various defect concentrations is estimated. The density of states of σ electrons at the Fermi level is calculated using the dependence of the slope-dH_c2/dT on ρ_n and a band structure model. It is impossible to estimate this density of states directly, because the upper critical field is determined by the carriers of one band, whereas the resistivity depends on the carriers in both bands.     

“Negative” gap in the spectrum of localized states of (In<Subscript>2</Subscript>O<Subscript>3</Subscript>)<Subscript>0.9</Subscript>(SrO)<Subscript>0.1</Subscript>

The reflection R(?ω), transmission t(?ω), absorption α(?ω), and refraction n(?ω) spectra of polycrystalline In₂O₃–SrO samples with low optical transparency, which contain In₂O₃ and In₂SrO₄ crystallites with In₄SrO_{6 + δ} interlayers, are examined. In the region of small ?ω values, the reflection coefficient decreases as the resistance of samples saturated with oxygen increases. Spectral dependences n(?ω) and α(?ω) are calculated using the classical electrodynamics relations. The results are compared to the data based on the t(?ω) spectra. The calculated absorption spectra are interpreted within the model with an overlap of tails of the density of states in the valence band and in the conduction band. A “negative” gap E _gn in the density of states with a width from–0.12 to–0.47 eV is formed in highly disordered samples in this model. It is demonstrated that the high density of defects and the band of deep acceptor states of strontium in the major matrix In₂O₃ phase are crucial to tailing of the absorption edge and its shift toward lower energies. The direct gap E _gd = 1.3 eV corresponding to the In₂SrO₄ phase is determined. The energy band diagram and the contribution of tunneling, which reduces the threshold energy for interband optical transitions, are discussed.     

X-ray spectra and electronic band structure of nitrogen in Al<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ga<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>N solid solid solutions

The electronic energy structure of the valence band and the x-ray absorption near edge structure (XANES) region of nitrogen in Al _x Ga_1?x N solid solutions and binary crystals of gallium nitride GaN and aluminum nitride AlN are calculated using the local coherent potential method and the cluster version of the muffin-tin approximation within the framework of the multiple scattering theory. It is demonstrated that the calculated electron densities of states correlate with the nitrogen K x-ray emission and nitrogen K x-ray absorption spectra. The electronic energy structure of the top of the valence band and the XANES region in Al _x Ga_1?x N solid solutions are compared with those in the binary crystals of the GaN and AlN nitrides, and an interpretation of their specific features is proposed. An analogy is drawn between the evolution of the electronic energy structure of the valence band and the XANES region in the alloys under investigation and the evolution of the electronic band structure in the Al _x B_1?x N and B _x Ga_1?x N alloys. General trends in the transformation of the structure and variations in properties of these alloys are discussed.     

Atomic and Electronic Structures of Metal-Rich Noncentrosymmetric ZrO<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>

The atomic and electronic structures of metal-rich noncentrosymmetric zirconium oxide synthesized by the ion beam sputtering of a metallic target in an oxygen atmosphere has been studied by X-ray photoelectron spectroscopy, Raman scattering, spectral ellipsometry, and quantum-chemical simulation. It has been established that ZrO_{x < 2} consists of ZrO₂, metallic Zr, and zirconium suboxides ZrO_y. The stoichiometry parameter of ZrO_y has been estimated. It has been shown that the optical properties of ZrO_{x < 2} are determined by metallic Zr. A model of fluctuation of the width of the band gap and a potential for electrons and holes in ZrO_{x < 2} based on spatial fluctuations of the chemical composition has been proposed.     

Dominant Majorana bound energy and critical current enhancement in ferromagnetic-superconducting topological insulator

Among the potential applications of topological insulators, we theoretically study the coexistence of proximity-induced ferromagnetic and superconducting orders in the surface states of a 3-dimensional topological insulator. The superconducting electron-hole excitations can be significantly affected by the magnetic order induced by a ferromagnet. In one hand, the surface state of the topological insulator, protected by the time-reversal symmetry, creates a spin-triplet and, on the other hand, magnetic order causes to renormalize the effective superconducting gap. We find Majorana mode energy along the ferromagnet/superconductor interface to sensitively depend on the magnitude of magnetization m _zfs from superconductor region, and its slope around perpendicular incidence is steep with very low dependency on m _zfs . The superconducting effective gap is renormalized by a factor η(m _zfs ), and Andreev bound state in ferromagnet-superconductor/ferromagnet/ferromagnet-superconductor (FS/F/FS) Josephson junction is more sensitive to the magnitude of magnetizations of FS and F regions. In particular, we show that the presence of m _zfs has a noticeable impact on the gap opening in Andreev bound state, which occurs in finite angle of incidence. This directly results in zero-energy Andreev state being dominant. By introducing the proper form of corresponding Dirac spinors for FS electron-hole states, we find that via the inclusion of m _zfs , the Josephson supercurrent is enhanced and exhibits almost abrupt crossover curve, featuring the dominant zero-energy Majorana bound states.     

Ionization of deep quantum wells: Optical trampoline effect

A new mechanism of transitions of an electronic system from the ground state to states with excitation energies exceeding many times the energy of a light photon initiating the transitions has been considered. This mechanism is based on the so-called optical “trampoline” effect: one of the interacting electrons receives energy from another electron and, simultaneously absorbing a photon ?ω, overcomes the energy gap significantly exceeding ?ω. Ionization of deep quantum wells by low-frequency light of moderate intensity due to the optical trampoline effect was calculated.     

Excitons in monoclinic zinc diphosphide: The <Emphasis Type="Italic">A</Emphasis>-exciton series and Fano effect

The A-exciton series in the absorption spectra of β-ZnP₂ monoclinic zinc diphosphide samples is investigated at different directions of the wave vector and different polarization states of radiation. It is shown that the oscillator strengths determined for the observed transitions are adequately described by the relationship F _n ∝n^?3 characteristic of S-type exciton states. The assumption is made that the A-exciton series is associated with the partially allowed dipole transitions to nS states of the orthoexciton with Γ ₂ ^? (x) symmetry at m _s =0. These states are mixed, to a first approximation, with nS states of the Γ ₂ ^? (z) singlet exciton due to the spin-orbit 2 interaction and are split off by the long-range (nonanalytical) part of the exchange interaction. The Fano antiresonances arise in the absorption spectra at resonances of the A-exciton series when the radiation vector E (or the induction vector D) has a component along the crystallographic axis c. These antiresonances are induced by the configurational interaction of discrete exciton states of the A series with the continuum of the exciton-phonon spectrum due to indirect transitions to the 1S band of the singlet exciton with phonon emission.     

Waves in a superlattice with arbitrary interlayer boundary thickness

The transmittance D(ω), reflectance R(ω), and dispersion ω(k) are investigated for waves of various nature propagating through a one-dimensional superlattice (multilayer structure) with arbitrary thickness of the interlayer boundary. The dependences of the band gap widths δω_m and their positions in the wave spectrum of the superlattice on the interlayer boundary thickness d and the band number m are calculated. Calculations are performed in terms of the modified coupled-mode theory (MCMT) using the frequency dependence of R(ω), as well as in the framework of perturbation theory using the function ω (k), which made it possible to estimate the accuracy of the MCMT method; the MCMT method is found to have a high accuracy in calculating the band gap widths and a much lower accuracy in determining the gap positions. It is shown that the m dependence of δω _m for electromagnetic (or elastic) waves is different from that for spin waves. Furthermore, the widths of the band gaps with m=1 and 2 are practically independent of d, whereas the widths of all gaps for m>2 depend strongly on d. Experimental measurements of these dependences allow one to determine the superlattice interface thicknesses by using spectral methods.     

Photoluminescence in germanium with a quasi-equilibrium dislocation structure

The dislocation-related photoluminescence of n-Ge single crystals with a quasi-equilibrium structure of 60° dislocations is investigated at a temperature of 4.2 K. It is shown that the dislocation-related photoluminescence spectra are described by a set involving from 8 to 13 Gaussian lines with a width of less than 15 meV. With due regard for the data available in the literature, the Gaussian lines with maxima at energies in the range 0.47 < E _m ≤ 0.55 eV are assigned to the emission of 90° Shockley partial dislocations involved in quasiequilibrium segments of 60° dislocations with different values of the stacking fault width Δ (Δ = Δ₀, Δ < Δ₀, and Δ > Δ₀). It is revealed that the d8 line at the energy E _m = 0.513 eV, which corresponds to the emission of straight segments with the equilibrium stacking fault width Δ₀, dominates in the photoluminescence spectra only at dislocation densities N _D < 10⁶ cm^?2. As the dislocation density N _D increases, the intensity of the d8 line decreases with the d7 line (E _m ≈ 0.507 eV) initially and the d7 and d6 lines (E _m ≈ 0.501 eV) then becoming dominant in the photoluminescence spectrum. The d7 and d6 lines are attributed to the emission of segments with stacking fault widths Δ < Δ₀. Possible factors responsible for the formation of stacking faults with particular widths Δ ≠ Δ₀ for quasi-equilibrium dislocations are discussed.     

Refractometry of mechanically compressed (NH<Subscript>4</Subscript>)<Subscript>2</Subscript>SO<Subscript>4</Subscript> crystals

The effect of uniaxial mechanical pressure σ _m ≤ 150 bar on the spectral (300–800 nm) dependence of the birefringerence Δn _i and refractive indices n _i of (NH₄)₂SO₄ crystals has been investigated. It is shown that the dispersion of n _i (λ) and Δn _i (λ) is normal and sharply increases with approach to the absorption edge. It is established that uniaxial pressure does not change the character of the dispersions dn _i /dλ and dΔn _i /dλ and only affects their magnitudes. It is shown that the increase in the refractive indices under uniaxial stress is mainly due to the increase in the refraction caused by the increase in the band gap and long-wavelength shift of the UV absorption band maximum.     

Reconstruction of the conduction band in metallic hydrogen sulfide

The theory of the normal properties of a metal generalized to the case of particular properties of an electron band with a finite width for electron–phonon systems with a varying electron density of states has been used to study the normal state of the SH₃ phase of hydrogen sulfide at a pressure of 225 GPa and a temperature of 200 K. The frequency dependences of the real, ReΣ(ω), and imaginary, ImΣ(ω), parts of the selfenergy part of the Green’s function of the electron Σ(ω), as well as the electron density of states N(ε) of the Im–3m stable orthorhombic structure of SH₃ hydrogen sulfide at a pressure of P = 225 GPa, which is renormalized by the strong electron–phonon coupling, have been calculated. It has been established that a part of the electron conduction band of the SH₃ phase of hydrogen sulfide adjacent to the Fermi level undergoes renormalization-induced reconstruction in the form of a number of energy pockets with the widths equal to fractions of the characteristic phonon energies of the system.     

Yields of multiparticle photoneutron reactions on the <Superscript>209</Superscript>Bi isotope

The relative yields of multiparticle photoneutron reactions on the ²⁰⁹Be isotope with emission of two to seven neutrons from the nucleus are measured. The experiment was carried out with the bremsstrahlung beam from the RTM-70 pulsed race-track microtron (INP, MSU) with a maximum photon energy E _γ ^m = 67.7 MeV.     

Coulomb Problem for <Emphasis Type="Italic">Z</Emphasis> &gt; Z<Subscript>cr</Subscript> in Doped Graphene

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Z_cr(J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z < Z_cr (J, n = 0), the energy of a level is presented as a function of charge Z for the lowest values of orbital angular momentum M, the level with J = 0 being the first to descend to the band edge. For Z>Z_cr (J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions ε₀ and widths γ of quasistationary states as a function of supercriticality. The values of ε₀* and width γ* are pointed out for which quasidiscrete levels may show up as Breit–Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Z_cr. In this single-particle approximation, there is no spontaneous creation of electron–hole pairs, and the impurity charge cannot be screened by this mechanism.     

Laser spectroscopy of Eu<Superscript>3+</Superscript> cubic centers in the CaF<Subscript>2</Subscript> bulk single crystal

The optical transitions ⁵ D _{0, 1} → ⁷ F _J (J = 0, 1, ..., 6) of Eu³⁺ cubic centers in the CaF₂ single crystal are investigated using combined excitation and emission spectroscopy at different time delays after the excitation pulse. The energies of the Stark sublevels of the ⁷ F _J ground states are determined.     

Relaxation processes upon photoexcitation of semiconductor CdF<Subscript>2</Subscript> by laser pulses

The microwave-cavity-based technique is used to study the processes of photoionization of electrons from donor levels to the conduction band in semiconductor CdF₂ crystals doped with Y, In, or Ga. The samples were excited by periodic pulses of Nd-laser (λ = 1.06 μm, pulse width ～10 ns) in the temperature range 6–77 K. The transient processes were detected in the absorption and dispersion modes related to variation of the imaginary and real parts of the complex permittivity ?₁ ? i?₂ induced by the light pulses. The observed signals consisted of short peak at t ～ 0, approximately 40–70 ns in length, and a long tail with a duration of ～100 ms. The short peak is likely to be related to the stay of the photoexcited carriers in the conduction band, while the long tail is associated with the processes of excitation relaxation after the electrons coming back to the donor levels of the impurity band. The weak temperature dependence of the width of the peak at t ～ 0 is explained by the tunneling mechanism of relaxation of electrons through the energy (or, probably, spatial) barrier separating the bound and free states of the carriers in the semiconductor CdF₂.     

Optical properties and mechanisms of current flow in Cu<Subscript>2</Subscript>ZnSnS<Subscript>4</Subscript> films prepared by spray pyrolysis

Thin films Cu₂ZnSnS₄ (up to 0.9 μm thick) with p-type conductivity and band gap E_g = 1.54 eV have been prepared by the spray pyrolysis of 0.1 M aqueous solutions of the salts CuCl₂ · 2H₂O, ZnCl₂ · 2H₂O, SnCl₄ · 5H₂O, and (NH₂)₂CS at a temperature T_S = 290°C. The electrophysical properties of the films have been analyzed using the model for polycrystalline materials with electrically active grain boundaries. The energy and geometric parameters of the grain boundaries have been determined as follows: the height of the barriers is E_b ≈ 0.045–0.048 eV, and the thickness of the depletion region is δ ≈ 3.25 nm. The effective concentrations of charge carriers p₀ = 3.16 × 10¹⁸ cm^–3 and their mobilities in crystallites μ_p = 85 cm²/(V s) have been found using the technique for determining the kinetic parameters from the absorption spectra of thin films at a photon energy hν ≈ E_g. The density of states at grain boundaries N_t = 9.57 × 10¹¹ cm^–2 has been estimated.