Isotope effect for the thermal expansion coefficient of germanium

The first experimental and theoretical investigation of the difference in the temperature behavior of the linear expansion coefficients of single crystals grown from isotopically highly enriched and natural germanium is reported. A comparison of the data for ⁷⁰Ge and ^natGe crystals reveals the significant influence of isotopic composition over a wide range of temperatures 30–230 K. Zh. éksp. Teor. Fiz. 115, 243–248 (January 1999)     

Isotope effect in the thermal conductivity of germanium single crystals

The thermal conductivity of chemically, structurally, and isotopically highly pure germanium single crystals is investigated experimentally in the temperature range from 2 to 300 K. It is found that the thermal conductivity of germanium enriched to 99.99% ⁷⁰Ge is 8 times higher at the maximum than the thermal conductivity of germanium with the natural isotopic composition. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 463–467 (25 March 1996)     

Low-temperature thermal conductivity of highly enriched and natural germanium

Experimental data on the thermal conductivity K(T) of crystals of natural and highly enriched germanium (99.99%) ⁷⁰Ge with lapped and polished surfaces are analyzed in the temperature range ∼1.5–8 K. In all the samples in the temperature range ∼1.5–4 K the standard boundary mechanism of scattering dominates. As the temperature is raised, an isotopic scattering mechanism is observed in the natural samples. In the highly enriched samples the theoretical values of K(T) turn out to be much smaller than the experimental ones. It is conjectured that a Poiseuille viscous flow regime of the phonon gas emerges in this case. Zh. éksp. Teor. Fiz. 114, 1757–1764 (November 1998)     

Characteristic features of the low-temperature thermal conductivity of highly-enriched and natural germanium

Experimental data on the thermal conductivity K(T) of natural and highly enriched (99.99%) Ge⁷⁰ crystals with ground and polished surfaces are analyzed in the temperature interval ∼2–8 K. In all samples, the boundary scattering mechanism predominates in the interval from 2 to 4.0 K. As temperature increases, in highly enriched samples N processes start to contribute to phonon transport and the behavior of K(T) corresponds to viscous Poiseuille flow of a phonon gas. The isotopic scattering mechanism plays a large role in isotopically nonideal samples. Fiz. Tverd. Tela (St. Petersburg) 40, 1604–1607 (September 1998)     

Low-field anomalous muonium depolarization in isotopically enriched germanium

The depolarization rate of anomalous muonium, Mu^*, in germanium isotopically enriched in⁷⁴Ge (I=0) was measured as a function of field. The concentration of⁷³Ge (I=9/2) was about 9 times less than natural abundance. The depolarization rate at 10 K in this isotopically enriched crystal for both lines of those Mu^* centers whose symmetry axes make an angle of 90° to the field is less than 1sec^–1 at all fields down to the lowest one measured, 14.5 gauss. This is in sharp contrast to the wide lines reported at low field in germanium having natural isotopic abundance. The spectrum of Mu^* in the isotopically enriched Ge crystal was also seen at zero field. These results confirm that the increased depolarization rate for Mu^* at low fields arises from unresolved nuclear hyperfine structure. The depolarization rates observed were consistent with an average hyperfine interaction with a single⁷³Ge nucleus of 2.5 MHz, a value requiring nearly 1% of the spin density to be on a typical atom.     

Near-IR laser inelastic electronic light scattering spectroscopy on transitions between ground and excited states of acceptor centers in GaAs and InP crystals

We report the development of a method for recording the low-temperature (T=6 K) near-IR inelastic light scattering spectra and the observation of electronic scattering on the transitions 1s _3/2(Γ₈) → 2s _3/2(Γ₈) between the ground and excited states of different shallow acceptor centers in a n-type semi-insulating crystal si-GaAs (n=1.0 × 10⁸ cm⁻³) and in a doped p-InP crystal (p=3.6×10¹⁷ cm⁻³). Moreover, a new line, associated with the transition 1s _3/2(Γ ₈) → 2p _3/2(Γ₈) and due to a dielectric local mode, recorded for the first time in the spectra of narrow-gap semiconductors, was found in the residual-frequency band in the p-InP spectrum between TO(Γ) and LO (Γ) phonons. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 5, 334–339 (10 March 1998)     

Quantum beats in excitons in Cu2O

A theoretical study is carried out of quantum beats (QB) in the time-dependent intensities of absorption of a test pulse and of spontaneous luminescence in a Cu₂O crystal under conditions of double optical resonance. It is assumed that pumping is effected by a CO₂-laser pulse which dynamically couples the exciton levels 1s(Γ ₅ ⁺ ) and 2p(Γ ₄ ⁻ ,Γ ₅ ⁻ ,Γ ₃ ⁻ Γ ₂ ⁻ ) and splits them into two or three pairs of quasi-energy levels. The frequency of the test pulse is in resonance with the frequency Γ ₅ ⁺ of the exciton. The corresponding intensities for various directions of the electric vector of the pump field E _L, the polarization vector ξ, and the wave vector q of the test pulse are obtained. The frequency of the quantum beats is twice the Rabi frequency, which for different values of E _L, ξ and q contains different sets of matrix elements of the dipole transitions between the levels 1s(Γ ₅ ⁺ ) and 2p(Γ ₄ ⁻ ,Γ ₅ ⁻ ,Γ ₃ ⁻ Γ ₂ ⁻ ). Thus, by measuring the period of the quantum beats it is possible to determine the unknown matrix elements of the indicated transitions. Fiz. Tverd. Tela (St. Petersburg) 39, 844–847 (May 1997)     

IR absorption and Raman spectra of single crystals of stable germanium isotopes

The Raman and IR absorption spectra of single crystals of germanium isotopes ⁷²Ge, ⁷³Ge, ⁷⁴Ge, and ⁷⁶Ge in the region of phonon absorption and interband electronic transitions are studied at room temperature. The dependence of the Raman peak position on the atomic mass has the form ν ~ M^–1/2. The shifts of the phonon absorption peaks of individual isotopes with respect to germanium of natural isotopic composition ^natGe are determined. With increasing average atomic mass of germanium, these peaks shift to longer wavelengths. In the region of interband electronic transitions, the intrinsic absorption edge of ⁷⁶Ge is observed to shift by 1 meV to higher energies with respect to Ge of natural isotopic composition. For isotopes with atomic masses close to that of natural germanium (⁷²Ge,⁷³Ge, ⁷⁴Ge), we found no significant difference in the band gap width at room temperature.     

Effect of isotopic disorder on the thermal conductivity of germanium in the region of the maximum

This paper discusses the question of how isotopic disorder affects the position of the thermal-conductivity maximum of germanium. The discussion is in terms of a Callaway-type model. Experimental data on the thermal conductivity of a natural Ge crystal and of highly enriched Ge⁷⁰ crystals are analyzed. Fiz. Tverd. Tela (St. Petersburg) 41, 1185–1189 (July 1999)     

Effect of isotopic composition on the linear thermal expansion coefficient of a germanium crystal lattice

Features of the thermal expansion coefficient α(T) of crystal lattices with different isotopic compositions have been analyzed. The case of germanium lattices has been studied in detail. Zh. éksp. Teor. Fiz. 114, 654–668 (August 1998)     

AdS solutions in gauge supergravities and the global anomaly for the product of complex two-cycles

Cohomological methods are applied for the special set of solutions corresponding to rotating branes in arbitrary dimensions, AdS black holes (which can be embedded in ten or eleven dimensions), and gauge supergravities. A new class of solutions is proposed, the Hilbert modular varieties, which consist of the 2n-fold product of the two-spaces H ⁿ /Γ (where H ⁿ denotes the product of n upper half-planes, H ², equipped with the co-compact action of Γ⊂SL(2,ℝ) ⁿ ) and (H ⁿ )^∗/Γ (where (H ²)^∗=H ²∪{cusp of Γ} and Γ is a congruence subgroup of SL(2,ℝ) ⁿ ). The cohomology groups of the Hilbert variety, which inherit a Hodge structure (in the sense of Deligne), are analyzed, as well as bifiltered sequences, weight and Hodge filtrations, and it is argued that the torsion part of the cuspidal cohomology is involved in the global anomaly condition. Indeed, in the presence of the cuspidal part, all cohomology classes can be mapped to the boundary of the space and the cuspidal contribution can be involved in the global anomaly condition.     

Raman scattering of light by optical phonons in Si-Ge-Si structures with quantum dots

Raman scattering of light by optical phonons in Si-Ge-Si structures with pseudomorphic germanium quantum dots has been investigated. Resonance amplification of the scattering intensity on E ₀ (Γ₇−Γ₈) transitions has been observed. It is shown that as a result of the formation of the layer of germanium quantum dots, the resonance energy is ∼0.3 eV higher than in the two-dimensional case. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 3, 203–207 (10 August 1996)     

Lattice dynamics investigations of SiGe core-shell nanowires

We present results from lattice dynamics calculations on the phonon modes and specific heat of SiGe core-shell nanowires. The results show that phonon dispersion relation of SiGe nanowires consists of four acoustic branches. The frequency of the first optical mode at Γ point shifts to low frequency as the Ge concentration is increasing. There are three strong peaks in the spectra of density of states. The peaks at 9.0 THz and 15.0 THz can be attributed to the high frequency Ge-Ge and Si-Si bond vibration. The broad peak around 3.0 THz of pure silicon nanowire corresponds to the transverse acoustic branch of bulk silicon. Moreover, specific heat of SiGe nanowires increases (decreases) with the increase of the concentration x at low (high) temperature. The specific heat at 300 K can be fitted by C _V = x ² C _Ge + (1 − x)C _Si, where C _Ge and C _Si are specific heat of pure germanium and silicon nanowires respectively.     

Values of adsorption and surface concentrations of the components in Na-K-Cs alloys

The values of adsorption Γ _i ^(N) and surface concentration X _i ^ω of all the components in alloys of the Na-K-Cs system were determined. The adsorption of cesium Γ_Cs^(N) was found to be > 0, while that for sodium Γ_Na^(N) was < 0 in all ternary alloys. The adsorption of potassium was found to undergo inversion when passing from Γ_K^(N) > 0 in ternary alloys (the ratios being X _Na: X _Cs > 14.4 and X _Cs < 6.5 at %) to the negative value of adsorption Γ_K^(N) in the alloys with X _Na: X _Cs < 14.4 and any cesium concentrations. Using the Na-K-Cs system, it was demonstrated for the first time that conditions ΣΓ _i ^(N) = 0 and ΣX _i ^ω = 1 and are fulfilled in ternary alloys.     

Bistability of quantum magnetotransport in a multilayer Ge/p-Ge1−x Six heterostructure with wide potential wells

Two metastable states of a multilayer Ge/p-Ge_1−x Si_x heterosystem with wide (∼ 35 nm) potential wells (Ge) are observed in strong magnetic fields B at low temperatures. In the first state, the Hall resistivity exhibits an inflection near the value ρ_xy=h/e ² scaled to one Ge layer. The longitudinal magnetoresistivity ρ_xx(B) possesses a minimum in the range of fields where this inflection occurs. The temperature evolution of the inflection in ρ_xy(B), the minimum of ρ _xx(B), and the value of ρ_xy at the inflection indicates a weakly expressed state of the quantum Hall effect with a uniform current distribution over the layers. In the second metastable state, an unusually wide plateau near h/2e ² with a very weak field dependence is observed in ρ_xy(B). Estimates show that in these samples the Fermi level lies below but close to the top of the inflection in the bottom of the well. For this reason, the second state can be explained by separation of a hole gas in the Ge layers into two sublayers, and the saturation of ρ_xy(B) near h/2e ² can be explained by the formation of a quantum Hall insulator state. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 4, 290–297 (25 August 1999)     

Structure of turbulent flows of incompressible fluids and the parametrization of turbulence

The structure of stationary isotropic, homogeneous turbulence in an incompressible fluid with Re ≫ 1 set into motion by a force with amplitude f ₀ and spatial and temporal time scales of r ₀ and τ ₀, respectively, is examined. It is found that, depending on the magnitude of the force that sets the fluid into motion, three fundamentally different turbulent stationary states of the fluid can develop and the dimensionless parameters responsible for transitions from one state to another, γ=f ₀ τ ₀ ² /r ₀ and Γ=γ ^4/3 Re, are determined. It is shown that for γ≪1 and Γ≪1 a Kolmogorov spectrum with E(k)∝1/k ^5/3 develops in the inertial range. During the transition to turbulent flows driven by large amplitude forces f ₀, i.e., during the transition to a regime with γ≪1 and Γ ≫ 1, a segment of the spectrum with E(k)∝1/k ² develops near the viscous range and “detaches” the Kolmogorov spectrum from the viscous range. Further increases in the amplitude f ₀ of the force, i.e., approaching the parameter range with γ≫1 and Γ≫1, causes the entire inertial range to be “occupied” by a spectrum E(k)∝1/k ², and outside the inertial range, large scale structures with a characteristic size extending to γ ^2/5 r ₀ begin to be generated. In the regime with Γ≪1, the power dissipated per unit mass of fluid is independent of the viscosity, but on going to turbulent regimes with Γ≫1, the viscous losses begin to depend on the viscosity of the fluid. The “turn-off” of viscous dissipation for Γ≫1 shows that a drag crisis can occur simply as the source power is increased, without any further conditions. With this method for the excitation of turbulence, the Loitsyanskii integral diverges for arbitrary values of γ and Γ. A physical mechanism is proposed to explain the readjustment of the spectrum of the turbulent fluctuations at different γ and Γ. These results have all been obtained neglecting intermittency. Zh. éksp. Teor. Fiz. 116, 1630–1647 (November 1999)     

Valence instability of uranium in U(Al1−x Gex)3

The electronic structure of U and Ge in the solid solutions U(Al_1−x Ge_x)₃ is investigated by measuring x-ray line shifts. It is shown that uranium has the mixed valence U³⁺ [Rn](5f ³)-U⁴⁺ [Rn](5f ²) over the entire composition range (0⩽x⩽1) and that the population of the uranium 5f shell increases by ∼0.28 5f electrons/U atom from UAl₃ (x=0) to UGe₃ (x=1). The electronic structure of Ge is close to the electronic structure of Ge metal over the entire composition range 0<x⩽1. No variation of the population of the Ge 4p shell is detected to within the experimental error (∼0.1 4p electrons/Ge atom) as the composition varies from x=0.2 to 1. It is established that the delocalization of a U 5f electron occurs as a result of its transition to the s or d band of the same uranium atom. Fiz. Tverd. Tela (St. Petersburg) 39, 1505–1508 (September 1997)     

A Riemann–Roch Theorem¶for One-Dimensional Complex Groupoids

We consider a smooth groupoid of the form Σ⋊Γ, where Σ is a Riemann surface and Γ a discrete pseudogroup acting on Σ by local conformal diffeomorphisms. After defining a K-cycle on the crossed product C ₀(Σ)⋊Γ generalising the classical Dolbeault complex, we compute its Chern character in cyclic cohomology, using the index theorem of Connes and Moscovici. This involves in particular a generalisation of the Euler class constructed from the modular automorphism group of the von Neumann algebra L ^∞(Σ)⋊Γ. Received: 1 February 2000 / Accepted: 3 December 2000     

Measurement of the cross sections for the production of the isotopes <Superscript>74</Superscript>As, <Superscript>68</Superscript>Ge, <Superscript>65</Superscript>Zn,and <Superscript>60</Superscript>Co from natural and enriched germanium irradiated with 100-MeV protons

The cross sections for the production of the radioactive isotopes ⁷⁴As, ⁶⁸Ge, ⁶⁵Zn, and ⁶⁰Co in metallic germanium irradiated with 100-MeV protons were measured, the experiments being performed both with germanium of natural isotopic composition and germanium enriched in the isotope ⁷⁶Ge. The targets were irradiated with a proton beam at the facility for the production of radionuclides at the accelerator of the Institute for Nuclear Research (INR, Moscow). The data obtained will further be used to calculate the background of radioactive isotopes formed by nuclear cascades of cosmic-ray muons in new-generation experiments devoted to searches for the neutrinoless double-beta decay of ⁷⁶Ge at underground laboratories.