Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

Spin susceptibility of neutron-irradiation-disordered YBa2Cu3O6.9 in the normal and superconducting states

The spin-spin relaxation rate ⁶³ T ₂ ⁻¹ of ⁶³Cu nuclei in CuO₂ layers is measured in the normal and superconducting states of the compound YBa₂Cu₃O_6.9 (T _c ^onset =94 K) subjected to radiation-induced disordering by a fast-neutron flux Φ to T _c ^onset =68 K (Φ=7×10¹⁸ cm⁻²) and T _c ^onset <4 K (Φ=12×10¹⁸ cm⁻²). It is found that as the structural disorder increases, the contribution of the indirect spin-spin interaction ⁶³ T _2G ⁻¹ , which is related to the value of the spin susceptibility at the boundary of the Brillouin zone of the copper planes χ_s(q={π/a; π/a}), decreases slightly at the transition to the superconducting state for the initial sample and remains unchanged for the weakly disordered sample. This behavior of the short-wavelength contribution to the spin susceptibility attests to the stability of the x ²−y ² symmetry of the energy gap against structural disorder, in accordance with proposed theoretical models of Cooper pairing for high-T _c cuprates. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 3, 172–177 (10 February 1998)     

One-dimensional localization in porous a-Si1−c Mnc

The temperature dependence of the conductance of porous silicon doped with manganese up to densities corresponding to the metallic side of the Anderson transition is investigated. It is found that in the temperature range below T=40–60 K the conductance decreases with T as G(T)∝T ^−1/3. This behavior corresponds to one-dimensional electron localization in silicon wires under conditions of inelastic electron-electron collisions with a small energy transfer. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 4, 265–269 (25 February 1998)     

Quenching of photoconductivity by a strong electric field in tin δ-doped GaAs structures

The conductivity of GaAs structures δ-doped with tin on the vicinal and singular faces was investigated in strong electric fields up to E=10⁴ V/cm and temperatures in the range 4.2 K <T<300 K. The measurements were performed in the dark and under illumination with visible light. Long-time photoconductivity of 2D electrons with threshold T _c ≈240 K was observed in samples which were δ-doped with tin on the vicinal face. A strong electric field not only quenches photoconductivity, but also increases the resistance of the structures at temperatures T<T _c by several orders of magnitude with respect to the dark resistance. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 5, 326–330 (10 March 1996)     

Isotope effect in charge transport of LuB12

The galvanomagnetic properties of single-crystal samples with various isotopic boron compositions have been investigated for the first time for the normal state of superconductor LuB₁₂ (T c ≈ 0.44 K). Precision measurements of the resistivity, Hall coefficient, and magnetic susceptibility have been performed over a wide temperature range of 2–300 K in magnetic fields up to 80 kOe. A change of the charge transport regime in this nonmagnetic compound with metallic conduction is shown to occur near T* ≈ 50−70 K. As a result, a sharp peak with significantly different amplitudes for Lu¹⁰B₁₂ and Lu¹¹B₁₂ is recorded in the temperature dependences of the Hall coefficient R _H(T) near T*. A significant (about 10%) difference (in absolute value) of the Hall coefficients R _H for the Lu¹⁰B₁₂ and Lu¹¹B₁₂ compounds at helium and intermediate temperatures has been found and the patterns of behavior of the dependence R _H(H) for T < T* in an external magnetic field H ≤ 80 kOe for Lu¹⁰B₁₂ and Lu¹¹B₁₂ are shown to differ significantly. Analysis of the Curie-Weiss contribution to the magnetic susceptibility χ(T) leads to the conclusion about the formation of magnetic moments μ_eff ≈ (0.13−0.19)μ_B in each unit cell of the fcc structure of LuB₁₂ compounds with various isotopic compositions. The possibility of the realization of an electronic topological 2.5-order transition near T* and the influence of correlation effects in the 5d-band on the formation of a spin polarization near the rare-earth ions in LuB₁₂ is discussed.     

Electronic phase separation in TmBa2Cu4O8

The NQR spectra of Cu(2) in the superconductor TmBa₂Cu₄O₈ are studied at temperatures from 300 to 4.2 K. In analyzing the spectra it is assumed that the NQR line of each isotope contains two Gaussian components — narrow (n) and broad (b). It is discovered that the NQR frequencies have a minimum at the temperature T*=150 K. The frequencies of the components of the spectrum are close at temperatures from T* to 4.2 K and differ substantially at temperatures T>T*. Both components are broadened as the temperature decreases, but this broadening occurs especially rapidly at temperatures T<T*. The relative intensity of the narrow component I _n/(I _n+I _b) equals 1/6 for T=225−160 K, increases abruptly at T=T*, and remains constant (1/3) at temperatures T from 125 to 4.2 K. Analysis of the experimental data showed that the anomalous temperature dependences of the Cu(2) NQR spectra could be due to electronic phase separation (stratification) in the CuO₂ planes at temperatures T⩽T*. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 3, 214–219 (10 February 1996)     

Insulator-metal transition in the single-crystal high-T c superconductor Bi-2201

Variations in the temperature behavior of resistivity, ρ(T), in the ab plane of the anisotropic single-crystal high-T _c superconductor BiSrCuO (2201 phase) have been observed at the insulator-metal (IM) transition. At low temperatures, as one approaches the transition, the Mott relation for two dimensions, ln ρ ∝ T ^−1/3, changes to ln ρ ∝ T ^−1/2, which corresponds to hopping conduction with a Coulomb gap in the density of states. Negative temperature slopes were revealed in the samples near the transition. Estimates suggest that superconductivity in these samples sets in from the Anderson insulator state. The behavior of the width of the superconducting transition and of the temperature of its onset, T _con, at the IM transition has been studied from measurements of the ac magnetic susceptibility. It is shown that in the vicinity of the IM transition the superconducting transition becomes broader, and the onset of the transition T _con shifts toward higher temperatures. This behavior is attributed to nonuniform superconductivity resulting from formation in the crystal of superconducting droplets with different values of T _c , which is caused by fluctuations in the local density of states due to the inherent disorder in the crystal. In these conditions, superconductivity has a percolation character. Fiz. Tverd. Tela (St. Petersburg) 40, 1190–1194 (July 1998)     

Electrical and galvanomagnetic properties of biocarbon preforms of white pine wood

The electrical and galvanomagnetic properties of high-porosity biocarbon preforms prepared from white pine wood by pyrolysis at carbonization temperatures T _carb = 1000 and 2400°C have been studied. Measurements have been made of the behavior with temperature of the electrical resistivity, as well as of magnetoresistance and the Hall coefficient in the 1.8–300-K temperature interval and magnetic fields of up to 28 kOe. It has been shown that samples of both types (with T _carb = 1000 and 2400°C) are characterized by high carrier (hole) concentrations of 6.3 × 10²⁰ and 3.6 × 10²⁰ cm⁻³, respectively. While these figures approach the metallic concentration, the electrical resistivity of the biocarbon materials studied, unlike that of normal metals, grows with decreasing temperature. Increasing T _carb brings about a decrease in electrical resistivity by a factor 1.5–2 within the 1.8–300-K temperature range. The magnetoresistance also follows a qualitatively different pattern at low (1.8–4.2 K) temperatures: it is negative for T _carb = 2400°C and positive for T _carb = 1000°C. An analysis of experimental data has revealed that the specific features in the conductivity and magnetoresistance of these samples are described by quantum corrections associated inherently with structural characteristics of the biocarbon samples studied, more specifically with the difference between the fractions of the quasi-amorphous and nanocrystalline phases, as well as with the fine structure of the latter phase forming at the two different T _carb.     

Thermal conductivity of crystalline fullerite C60 in the simple cubic phase

The behavior of the thermal conductivity k(T) of bulk faceted fullerite C₆₀ crystals is investigated at temperatures T=8–220 K. The samples are prepared by the gas-transport method from pure C₆₀, containing less than 0.01% impurities. It is found that as the temperature decreases, the thermal conductivity of the crystal increases, reaches a maximum at T=15–20 K, and drops by a factor of ∼2, proportional to the change in the specific heat, on cooling to 8 K. The effective phonon mean free path λ _p, estimated from the thermal conductivity and known from the published values of the specific heat of fullerite, is comparable to the lattice constant of the crystal λ _p∼d=1.4 nm at temperatures T>200 K and reaches values λ_p∼50d at T<15 K, i.e., the maximum phonon ranges are limited by scattering on defects in the volume of the sample in the simple cubic phase. In the range T=25−75 K the observed temperature dependence k(T) can be described by the expression k(T)∼exp(Θ/bT), characteristic for the behavior of the thermal conductivity of perfect nonconducting crystals at temperatures below the Debye temperature Θ (Θ=80 K in fullerite), where umklapp phonon-phonon scattering processes predominate in the volume of the sample. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 651–656 (25 April 1997)     

Sound propagation anomalies and phase diagram of chromium alloys

Calculations of the complex elastic moduli Ĉ(T) in dilute Cr alloys are compared to measurements of the velocity and damping of sound near T _N and at high temperatures T>T _N (T _N — Néel temperature). The thermodynamic calculation is based on the covalent bond model of 3d ions in a state with different numbers n of covalent electrons. The parameters A _ij ⁽ⁿ⁾ of indirect exchange between the ions of the i and j sublattices are expressed in terms of the covalent bond energy Γ _ij ⁽ⁿ⁾ . The stability of the charge and spin density waves (CDWs and SDWs) is found by a variational method and is determined by the dispersion of Γ _ij ⁽ⁿ⁾ and by the Coulomb parameters U _n. For a small structural vector Q the phase diagram contains a superantiferromagnetic phase (SAFM) at temperatures T _N<T≲2T _N. The peak of the defect |ΔE(T)| of the modulus and of the sound damping Δ_h(T _N) near the first-order SDW-SAFM transition is determined by the structure of the transitional domain. Measurements of the anomalous growth of E(T) at temperatures T>T _N make it possible to determine the magnetostriction constants λ(T) of Ce alloys in the SAFM phase on the basis of the SAFM theory. Fiz. Tverd. Tela (St. Petersburg) 41, 1467–1472 (August 1999)     

Growth of crystallites consisting of C60 molecules on heated (100)Mo

The initial stages of growth of films of C₆₀ molecules on a (100)Mo surface are studied by high-resolution Auger spectroscopy and atomic force microscopy under ultrahigh vacuum conditions. It is shown that at T<750 K, after a specific coating with molecular density 1.5×310¹⁴ cm⁻², which the authors term a high-temperature (HT) monolayer, has formed on the surface, crystallites in the form of “towers” with flat tops grow on the surface. The fraction of the area occupied by towers depends strongly on the substrate temperature and the flux density of the molecules on the surface but is virtually independent of the exposure time. At temperatures _T>760 K the C₆₀ molecules making up the crystallites desorb, while the molecules making up the HT monolayer decompose, and the carbon released is dissolved in the interior of the substrate. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 12, 969–972 (25 June 1998)     

Weak exchange interactions in the heteronuclear crystal CuPr2(CCl3COO)8·6H2O

The new heteronuclear crystal CuPr₂(CCl₃COO)₈·6H₂O, constructed of chains containing copper and praseodymium atoms, has been synthesized and investigated by EPR at 9.3 GHz at temperatures ranging from room temperature down to 10 K. At temperatures T∼300–130 K, EPR spectra are observed which are characteristic of isolated polyhedra of copper ions with g _z=2.330±0.005, g _x,y =2.053±0.005, A _z=139×10⁻⁴ cm⁻¹, and A _x,y <26×10⁻⁴ cm⁻¹. At temperatures T<130 K a complex spectrum is observed, associated with the appearance of weak exchange interactions between the copper ions in the chain (J _Cu-CuΣS _i·S _i+1), comparable in magnitude with the hyperfine interactions J _Cu-Cu=0.015 cm⁻¹ at T=10 K. The magnitude of the exchange interaction decreases smoothly as the temperature is raised. It is conjectured that orbitals of the praseodymium ions participate in the process of indirect exchange between the copper ions. Fiz. Tverd. Tela (St. Petersburg) 41, 2154–2157 (December 1999)     

Vortex pinning in YBa2Cu3O7?x films

Evidence that pinning on linear or planar defects dominates the vortex dynamics in YBa₂Cu₃O_7−x (YBCO) films is provided by complex impedance measurements at temperature 8 K<T<T _c and magnetic field 0<B<6 T. Below the vortex lattice melting transition B_g(T) but above a threshold field B_p≈8(1-T/T _c ) T, the inductance of vortices increases as B², much less rapidly than predicted for collective pinning of vortices by point defects. Above the vortex melting line, critical scaling persists over the region B_g(T<B<B^*(T) where the vortex correlation length ξ exceeds a characteristic length scale ξ^*≡ξ(B=B^*)≈450?. The value of ξ^* is not sensitive to Al-doping in the Cu sites in the lattice and is close to the size of twin domains in the film. The nature of the observed crossovers is discussed in terms of available theoretical models for a glass-liquid transition at B_g.     

The comparison of characteristics of π− mesons produced in central Mg-Mg interactions with the quark gluon string model predictions

A detailed study of pion production in central Mg-Mg collisions at a momentum of 4.3 GeV/c per incident nucleon was carried out with use of the setup GIBS. The average kinematical characteristics of pions (multiplicity n ₋, momentum P, transverse momentum P _T, emission angle Θ, rapidity Y) and corresponding distributions have been obtained. The experimental results have been compared with the predictions of the Quark Gluon String Model (QGSM) and satisfactory agreement between the experimental data and the model has been found. The QGSM reproduces also the dependence of average P _T on n ₋. The temperatures of π⁻ mesons have been estimated in the rapidity interval of 0.5 ≤ Y ≤ 2.1. A satisfactory fit for π⁻ mesons has been achieved by using a form involving two temperatures T ₁ and T ₂. It is found that the QGSM underestimates T ₂ by (10−15)%. The data have been analyzed using the transverse momentum technique. The observed dependence of the <P _x ^′(Y)> on Y shows the S-shape behaviour. The slope at midrapidity F has been determined. The QGSM reproduces the <P _x> distribution satisfactorily, but underestimates the parameter F. Received: 2 August 1997 / Revised version: 17 November 1997     

Electronic superconductor Pr2CuO4−x Fx: Magnetic correlations at high temperatures (150<T<600 K) according to 19F NMR data

The longitudinal and transverse relaxation rates of ¹⁹F nuclei in Pr₂CuO_4−x F_x (x=0.20) samples are measured at high temperatures (150 K<T<600 K). A feature is found in the temperature dependence of the relaxation rates at temperature T′≅300 K. The magnetic properties of the electronic superconductor Pr₂CuO_4−x F_x as a possible system with a stripe ordering of carriers and spins are discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 4, 328–332 (25 February 1997)     

Electron mobility in compensated VPE GaAs films

Electron Hall mobilities were measured on a series of intentionally compensated vapor phase epitaxy (VPE) GaAs layers. Using Sn and Zn as dopants, compensation ratiosK=(N_D+N_A)/(N_D-N_A) as high as 50 were obtained. Already for samples with the lowestK values the 300 K mobilities are higher than the 77 K values. In the range 20<T<100 [K] the data may be represented by μ∼T ^α with α increasing from 0.6 to 1.1 with compensation. The experimental μ values are smaller than those predicted from current models in all cases. It appears that scattering at ionized impurities is the dominant process also at temperatures well above 77 K, and that this scattering process is quantitatively underestimated in current models.     

Galvanomagnetic properties of the Al1−x Six nonequilibrium substitutional solid solutions

Galvanomagnetic characteristics of the A_1−x Si_x solid solutions (x<12 at. %) have been studied within a broad range of temperatures (1.8–290 K) and magnetic fields (up to 15 T). An anomaly in the concentration dependence of the Hall coefficient R _H (x,T=290 K) has been revealed near the boundary of absolute instability (x<8.5 at. %) of compounds in the Al_1−x Si_x series. The variation of the Hall coefficient and of the magnetoresistance in the A_1−x Si_x series at low (T<77 K) temperatures is analyzed within models taking into account the anisotropy in conduction-band electron scattering. Fiz. Tverd. Tela (St. Petersburg) 41, 3–10 (January 1999)     

Doppler shapes of the γ line in the <Superscript>9</Superscript>Be(α, nγ)<Superscript>12</Superscript>C reaction in plasma at temperatures <Emphasis Type="Italic">T</Emphasis><Subscript>α</Subscript> < 0.6 MeV

A parametrization of the partial cross section of the ⁹Be(α, nγ)¹²C reaction in the α-particle energy range of 0.3–7.9 MeV is presented, along with the count rates of γ quanta. The need to consider subbarrier (Eα < 1.9 MeV) α-particles in plasma for temperatures T _α < 0.2 MeV is substantiated. The shapes of the Doppler-broadened 4.44 MeV γ line and the count rates of γ quanta in the plasma of the JET tokamak are measured for the first time and compared to the calculated values. An estimated T _α ≲ 160 keV is obtained.     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

Elementary spin excitations in a Heisenberg S=1/2 antiferromagnet with Skyrmions

The elementary spin excitations in two-dimensional Heisenberg antiferromagnets with spin S=1/2 in a metastable, spatially inhomogeneous state are investigated. The energy spectrum of the excitations, the local order parameter, and the temperature dependence of the spin correlation length are found. It is shown that the results obtained can be used to explain the experimental data on neutron scattering in La₂CuO₄ at temperatures T>T _N. Fiz. Tverd. Tela (St. Petersburg) 39, 656–659 (April 1997)