Effect of the composition of the solid solution on the high-temperature microhardness of SiGe heteroepitaxial layers grown on Ge and Si substrates

The effect of the composition of epitaxial layers (ELs) of the Si_xGe_1?x solid solution grown on Ge and Si substrates on their microhardness and the length of dislocation rosettes forming around indentations is studied at a homologous temperature 0.5T_melt for each composition. For the Si_xGe_1?x/Ge (0≤x<0.15) and Si_xGe_1?x/Si (0.85<x≤1) ELs, the dependences of the microhardness and the length of dislocation rosettes on the solid-solution composition are nonmonotonic. The nonmonotonic change in the plasticity of the ELs is most likely caused by hardening of the solid solutions in a certain composition range due to their spinodal decomposition with the formation of clusters and disperse precipitates.     

Anisotropic<Emphasis Type="Italic">s</Emphasis>-wave or<Emphasis Type="Italic">d</Emphasis>-wave pairing? Analysis of experiments on ion irradiation of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7-x</Subscript> films

The effect of ion irradiation on the superconducting transition temperatureT _c and resistivityρ _ab (T) of YBa₂Cu₃O_7-x films with different oxygen content (initial temperatureT _c0≈90 K and 60 K) is studied experimentally. The dependenciesT _c /T _c0 on residual resistivityρ _o are obtained in very wide range 0.2<T _c /T _c0 <1 andρ _o μΩ·cm. The critical values ofρ _o , corresponding to the vanishing of superconductivity, are found to be an order of magnitude larger then those predicted by theory ford-wave pairing. At 0.5÷0.6<T _c /T _c0<1 the experimental data are in close agreement with theoretical dependencies, obtained for the anisotropics-wave superconductor within the BCS-framework.     

Effect of phase transitions on the exciton absorption spectrum of Rb<Subscript>x</Subscript>K<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ag<Subscript>4</Subscript>I<Subscript>5</Subscript> superionic conductors

The absorption spectrum of thin films of solid solutions of Rb_xK_1?xAg₄I₅ superionic conductors is investigated in the energy range 3–6 eV at temperatures from 90 to 290 K upon heating and cooling. It is established that the temperature dependences of the spectral position E _m and the half-width Γ of the long-wavelength exciton band are determined by the exciton-phonon interaction and the generation of Frenkel defects at phase transitions to the superionic state. Fluctuations of the composition of solid solutions do not affect the behavior of the dependences E _m (x) and Γ(x) at 90 K, which is indicative of the localization of excitons in the AgI sublattice of these compounds. A difference in the dependences T _c 1(x) and T _c 2(x) (the γ → β and β → α phase transitions, respectively) is revealed: the curve T _c 1(x) has a minimum at x ≈ 0.5, whereas the curve T _c 2(x) shows a weak maximum.     

Magnetic Properties of Composite Materials Based on a Solid Solution of Type (CuInSe<Subscript>2</Subscript>)<Subscript>1 – <Emphasis Type="Italic">x</Emphasis></Subscript>(MeSe)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> (Me = Mn,Fe) and Polyethylene

Basic magnetic characteristics (coercive force H_c, residual magnetization M_r, magnetization M, and saturation magnetization M_s) of solid solutions of type (CuInSe₂)_1–x(MeSe)_x (Me = Mn, Fe) have been investigated in a wide temperature interval (100–300 K). The existence of a magnetic phase transition has been established for all studied solid solutions at low temperatures, and the Néel temperatures have been determined from the temperature dependences of the magnetization. It is shown that the temperature dependences of coercive force H_c and of magnetization M can be described using the thermal relaxation (fluctuation) theory.     

The structure of a vortex line and the lower critical field in superconducting alloys

The structure of an isolated vortex line, and the lower critical fieldH _c 1, is calculated by means of the generalized Ginzburg-Landau (GL) theory for arbitrary values of the GL-parameterk(≧1/√2) and the mean free pathl at temperaturesT in the vicinity ofT _c . The free energy functional including the corrections of order [1?(T/T _c )] to the GL-functional is derived exactly. The corresponding Euler-Lagrange equations determining the zero-order (GL) contributions and the corrections of order [1?(T/T _c )] to the order parameter,f(r), and the superfluid velocity,v(r), have been solved numerically. The shapes of the first-order corrections off(r), v(r), and the magnetic field,h(r) are found to depend markedly, for a given value ofκ, on a second parameter,α=0.882(ξ ₀ /l) (whereξ ₀ is theBCS-coherence-distance). The deviations from the GL-solutions become largest forh(r) at parameter valuesk≈ 1 andα ≈ 0(the deviation ofh(0) is about 6% atT=0.9T _c forκ=1 andα=0). The ratioH _c1/H _c (where the thermodynamic criticalH _c has the BCS-temperature-dependence) is found to increase slightly in the “clean” limit (α=0), and to decrease slightly in the “dirty” limit (α=∞) asT decreases (the variation ofH _c 1/H _c is always less than 3% for arbitrary values ofκ andα asT decreases fromT _c to 0.9T _c ).     

Mechanism of charge transfer in <Emphasis Type="Italic">n</Emphasis>-CdS/<Emphasis Type="Italic">p</Emphasis>-CdTe heterojunctions

The capacitance-voltage and current-voltage characteristics of the n-CdS/p-CdTe heterosystem are investigated. Analysis of these characteristics demonstrates that the CdTe_1?x S _x solid solution formed at the n-CdS/p-CdTe heterointerface is inhomogeneous in both the conductivity and composition. The thickness of solid solutions is estimated from the capacitance-voltage characteristics. It is shown that, for the n-CdS/p-CdTe heterosystem, the current-voltage characteristic in the current density range 10^?8-10^?5 A cm^?2 is governed by the thermal electron emission, whereas the current in the heterostructure at current densities in the range 10^?4-10^?2 A cm^?2 is limited by recombination of charge carriers in the electroneutral region of the CdTe_1?x S _x solid solution. The lifetime and the diffusion length of minority charge carriers in the CdTe_1?x S _x solid solution and the surface recombination rate at the interface between the CdS layer and the CdTe_1?x S _x solid solution are determined. It is demonstrated that the n-CdS/p-CdTe heterostructure operates as a p-i-n structure in which CdTe is a p layer, CdTe_1?x S _x is an i layer, and CdS is an n layer.     

Almost mobility edges and the existence of critical regions in one-dimensional quasiperiodic lattices

We study a one-dimensional quasiperiodic system described by the Aubry–André model in the small wave vector limit and demonstrate the existence of almost mobility edges and critical regions in the system. It is well known that the eigenstates of the Aubry–André model are either extended or localized depending on the strength of incommensurate potential V being less or bigger than a critical value V _c , and thus no mobility edge exists. However, it was shown in a recent work that for the system with V < V _c and the wave vector α of the incommensurate potential is small, there exist almost mobility edges at the energy E _c±, which separate the robustly delocalized states from “almost localized” states. We find that, besides E _c±, there exist additionally another energy edges E _c′±, at which abrupt change of inverse participation ratio (IPR) occurs. By using the IPR and carrying out multifractal analyses, we identify the existence of critical regions among |E _c±|?≤?|E|?≤?|E _c′±| with the mobility edges E _c± and E _c′± separating the critical region from the extended and localized regions, respectively. We also study the system with V > V _c , for which all eigenstates are localized states, but can be divided into extended, critical and localized states in their dual space by utilizing the self-duality property of the Aubry–André model.     

Temperature Dependence of the Upper Critical Field in Disordered Hubbard Model with Attraction

We study disorder effects upon the temperature behavior of the upper critical magnetic field in an attractive Hubbard model within the generalized DMFT+Σ approach. We consider the wide range of attraction potentials U—from the weak coupling limit, where superconductivity is described by BCS model, up to the strong coupling limit, where superconducting transition is related to Bose–Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures significantly higher than superconducting transition temperature, as well as the wide range of disorder—from weak to strong, when the system is in the vicinity of Anderson transition. The growth of coupling strength leads to the rapid growth of H_c2(T), especially at low temperatures. In BEC limit and in the region of BCS–BEC crossover H_c2(T), dependence becomes practically linear. Disordering also leads to the general growth of H_c2(T). In BCS limit of weak coupling increasing disorder lead both to the growth of the slope of the upper critical field in the vicinity of the transition point and to the increase of H_c2(T) in the low temperature region. In the limit of strong disorder in the vicinity of the Anderson transition localization corrections lead to the additional growth of H_c2(T) at low temperatures, so that the H_c2(T) dependence becomes concave. In BCS–BEC crossover region and in BEC limit disorder only slightly influences the slope of the upper critical field close to T _c . However, in the low temperature region H_c2 (T may significantly grow with disorder in the vicinity of the Anderson transition, where localization corrections notably increase H_c2 (T = 0) also making H_c2(T) dependence concave.     

Structural and magnetic phase transformations in the BiFeO<Subscript>3</Subscript>-CaFe<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>O<Subscript>3</Subscript> system

The crystal structure and magnetic properties of the Bi_{1 ? x} Ca _x Fe_{1 ? x/2}Nb _x/2O₃ system were studied. It is shown that, at x ≤ 0.15, the unit-cell symmetry of solid solutions is rhombohedral (space group R3c). Solid solutions with x ≥ 0.3 have an orthorhombic unit cell (space group Pbnm). The rhombohedral compositions are antiferromagnetic, while the orthorhombic compositions exhibit a small spontaneous magnetization due to Dzyaloshinski?-Moriya interaction. In CaFe_0.5Nb_0.5O₃, the Fe³⁺ and Nb⁵⁺ ions are partially ordered and the unit cell is monoclinic (space group P2₁/n). In the concentration range 0.15 < x < 0.30, a two-phase state (R3c + Pbnm) is revealed.     

The anisotropic conductivity of two-dimensional electrons on a half-filled high Landau evel

We study the conductivity of two-dimensional interacting electrons on the half-filled Nth Landau level with N?1 in the presence of quenched disorder. The existence of the unidirectional charge-density wave state at temperature T<T _c , where T _c is the transition temperature, leads to the anisotropic conductivity tensor. We find that the leading anisotropic corrections are proportional to (T _c ?T)/T _c just below the transition, in accordance with the experimental findings. Above T _c , the correlations corresponding to the unidirectional charge-density wave state below T _c result in corrections to the conductivity proportional to \(\sqrt {{{T_c } \mathord{\left/ {\vphantom {{T_c } {T - T_c }}} \right. \kern-\nulldelimiterspace} {T - T_c }}} \).     

Critical magnetic field of the vortex-free state in NbC thin films and prospects for its observation in MgB<Subscript>2</Subscript>

The critical magnetic fields H _c‖ and H _c2 are measured for thin films of the isotropic superconductor NbC. It is revealed that the critical fields exhibit strong anisotropy due to the vortex-free state of the film in a magnetic field aligned parallel to its surface. The H _c‖/H _c2 ratio at 2 K exceeds 6 and increases with increasing temperature. The dependence H _c‖(T) agrees quantitatively with the concepts of microscopic theory on the vortex-free state of a thin film of a clean superconductor in the temperature range below T _c . As the electron mean free path decreases under irradiation of the film with a low dose of He⁺ ions, the critical field H _c‖ remains unchanged near T _c but increases significantly at lower temperatures. The well-known theoretical models are used to estimate the electronic parameters and thicknesses of MgB₂ films for which the specific features associated with the vortex-free state of the two-gap superconductor can manifest themselves in the temperature dependence of the critical magnetic field H _c‖(T).     

Dependence of the magnitude and direction of the persistent current on the magnetic flux in superconducting rings

The obtained periodic magnetic-field dependences I _c+(Φ/Φ₀) and I _c?(Φ/Φ₀) of the critical current measured in opposite directions on asymmetric superconducting aluminum rings has made it possible to explain previously observed quantum oscillations of dc voltage as a result of alternating current rectification. It was found that a higher rectification efficiency of both single rings and ring systems is caused by hysteresis of the current-voltage characteristics. The asymmetry of current-voltage characteristics providing the rectification effect is due to the relative shifts of the magnetic dependences I _c?(Φ/Φ₀) = I _c+(Φ/Φ₀ + Δ?) of the critical current measured in opposite directions. This shift means that the position of I _c+(Φ/Φ₀) and I _c?(Φ/Φ₀) minima does not correspond to n + 0.5 magnetic flux Φ quanta, which is in direct contradiction to measured Little-Parks resistance oscillations. Despite this contradiction, the amplitude I _{c, an}(Φ/Φ₀) = I _c+(Φ/Φ₀) ? I _c?(Φ/Φ₀) of critical current anisotropy oscillations and its variations with temperature correspond to the expected amplitude of persistent current oscillations and its variations with temperature.     

Weak ferromagnetism in BiFeO<Subscript>3</Subscript>-based multiferroics

The magnetic properties of the Bi_{1 ? x} Ln _x FeO₃ (Ln is a rare-earth ion), Bi_{1 ? x} A _x FeO_{3 ? x/2} (A is an alkali earth ion), and BiFe_{1 ? x} Ti _x O_{3 + δ} solid solutions in magnetic fields up to 14 T have been studied. The concentration ranges of the existence of the ferroelectric phase described by the space group R3c have been determined. It is shown that the substitution of the rare-earth ions for the Bi³⁺ ions leads to a sharp decrease in the critical fields inducing the metamagnetic transition from a modulated antiferromagnetic state to a weakly ferromagnetic one; however, the modulated structure in the concentration range of the R3c phase is mainly retained. The substitution of the alkali earth ions (x ～ 0.1) for the bismuth ions leads to the total destruction of the modulated structure and to the implementation of the weakly ferromagnetic state within the R3c phase. A homogeneous weakly ferromagnetic state has been revealed when the Ti⁴⁺ ions (x = 0.1) are substituted for the Fe³⁺ ions in the ferroelectric R3c phase.     

Enhancement of pseudogap anomalies induced by nanoscale structural inhomogeneity in YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>6.93</Subscript> high-<Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> superconductor

The magnetization M(H) in the superconducting state, dc magnetic susceptibility χ(T) in the normal state, and specific heat C(T) near the superconducting transition temperature T _c have been measured for a series of fine-crystalline YBa₂Cu₃O _y samples having nearly optimum values of y = 6.93 ± 0.3 and T _c = (91.5 ± 0.5) K. The samples differ only in the degree of nanoscale structural inhomogeneity. The characteristic parameters of superconductors (the London penetration depth and the Ginzburg–Landau parameter) and the thermodynamic critical field H _c are determined by the analysis of the magnetization curves M(H). It is found that the increase in the degree of nanoscale structural inhomogeneity leads to an increase in the characteristic parameters of superconductors and a decrease in H _c(T) and the jump of the specific heat ΔC/T _c. It is shown that the changes in the physical characteristics are caused by the suppression of the density of states near the Fermi level. The pseudogap is estimated by analyzing χ(T). It is found that the nanoscale structural inhomogeneity significantly enhances and probably even creates the pseudogap regime in the optimally doped high-T _c superconductors.     

Grundzustand eines Fermi-Gases mit hard-sphere-Wechselwirkung

The decomposition of the ground state wave function of a Fermi gas interacting via hard core potentials into cluster functionsS _n leads to a systematic expansion of wave function and energy in powers of the parameterc=P _F r _c (r _c =hard core radius,P _F =Fermi momentum). For instance,S _n has the order of magnitudec ^n-λ-1, if λ=number of Fermion coordinates with distances smaller thanr _c . The first three energy terms agree with the ones given by other authors. Any occurrence of singular terms in the intermediate steps of the derivation can be avoided     

Exponential Increase in the Resistivity upon Cooling and Superconductivity in Indium-Doped Pb<Subscript>0.45</Subscript>Sn<Subscript>0.55</Subscript>Te

We have analyzed the temperature and magnetic-field dependences of resistivity ρ(T, H) of semiconducting compound Pb_0.45Sn_0.55Te doped with 5 at % In under a hydrostatic compression at P < 12 kbar. It is found that the temperature dependence ρ(T) at all pressures at T < 100 K is exponential with the activation energy decreasing upon an increase in pressure; this is accompanied with a superconducting transition on the ρ(T) and ρ(H) dependences at P > 4.8 kbar at T > 1 K (T _c = 1.72 K at a level of 0.5ρ _N at P = 6.8 kbar). We consider the model describing the low-temperature “dielectrization” of the semiconducting solid solution and the formation of the superconducting state upon an increase in the hydrostatic compression P > 4 kbar.     

Temperature dependence of the upper critical field of superconducting alloys

The upper critical field,H _c2, is calculated in the temperature range close toT _c for arbitrary values of the mean free path 1. The method is to treat the fourth-order term in the linearized differential equation for the gap parameter as a perturbation to the harmonic oscillator equation. The Nambu-Tuan term, which determines the structure of the “clean-limit” and “dirty-limit” parts of the fourth-order term, is calculated by means of the ladder diagram technique for impurity interaction lines. The result is that the magnitude of the slope of the curveH _c2/√2H _c κ versust=T/T _c att=1 decreases monotonically from the value 0.41 to 0.12 as the ratio of the BCS coherence lengthξ ₀ to the mean free path 1 increases from 0 to ∞. For 1?ξ ₀ this slope is about 0.26.     

Superconducting transition temperature in hafnium under pressures up to 64 GPa

The superconducting transition temperature T _c of hafnium is measured as a function of pressure up to 64 GPa. The character of the pressure dependence of T _c observed at α–ω–β transitions in Hf is found to be similar to that observed for Zr. In the regions of α and β phases, T _c increases with pressure with the slopes dT _c /dP=0.05 and 0.16 K/GPa, respectively. At the α–ω transition, T _c (P) exhibits a tendency to a decrease, while at the ω–β transition, T _c increases stepwise from 5.8 to 8.0 K. The α–ω transition occurs at pressures between 31.2 and 35.9 GPa, and the ω–β transition, at a pressure of 62±2 GPa.     

Role of initial correlation in coarsening of a ferromagnet

We study the dynamics of ordering in ferromagnets via Monte Carlo simulations of theIsing model, employing the Glauber spin-flip mechanism, in space dimensionsd = 2 and3, on square and simplecubic lattices. Results for the persistence probability and the domain growth arediscussed for quenches to various temperatures (T _f ) below the criticalone (T _c ), from differentinitial temperatures T _i ≥T _c . In long timelimit, for T _i >T _c ,the persistence probability exhibits power-law decay with exponents θ ? 0.22 and? 0.18 in d = 2 and 3, respectively. For finite T _i , the early timebehavior is a different power-law whose life-time diverges and exponent decreases asT _i →T _c . The two steps areconnected via power-law as a function of domain length and the crossover to the secondstep occurs when this characteristic length exceeds the equilibrium correlation length atT =T _i . T _i =T _c is expected toprovide a new universality class for which we obtain θ ≡θ _c ? 0.035 ind = 2 and?0.105 in d = 3. The time dependenceof the average domain size ?, however, is observed to be rather insensitive tothe choice of T _i .