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)     

Implications of time-reversal symmetry for the band structure of single-wall carbon nanotubes

When electron states in carbon nanotubes are characterized by two-dimensional wave vectors with the components K ₁ and K ₂ along the nanotube circumference and cylindrical axis, respectively, then two such vectors symmetric about a M-point in the reciprocal space of graphene are shown to be related by the time-reversal operation. To each carbon nanotube there correspond five relevant M-points with the following coordinates: K ₁⁽¹⁾ = N/2R, K ₂⁽¹⁾= 0; K ₁⁽²⁾ = M/2R, K ₂⁽²⁾= −π/T; K ₁⁽³⁾= (2N −M)/2R, K ₂⁽³⁾= π/T; K ₁⁽⁴⁾= (M + N)/2R, K ₂⁽⁴⁾= -π/T, and K ₁⁽⁵⁾= (N − M)/2R, K ₂⁽⁵⁾= π/T, where M and N are the integers relating the chiral, C _h , symmetry, R, and translational, T, vectors of the nanotube by N R = C _h + M T, T = |T|, and R is the nanotube radius. The states at the edges of the one-dimensional Brillouin zone, which are symmetric about the M-points with K ₂ = ±π/T, are shown to be degenerate due to the time-reversal symmetry.     

Metal-insulator transition induced by a magnetic field in the compounds Eu0.7 A 0.3MnO3 (A=Ca, Sr)

The temperature R(T) and field R(H) dependences of the electrical resistance in the compound Eu_0.7 A _0.3MnO₃ (A=Ca, Sr) are investigated in the temperature range 4.2–200 K in magnetic fields up to 14 T. Above the antiferromagnetic transition temperature T _a, the function R(T) is semiconducting in character. Application of a magnetic field H that exceeds a certain critical value H _c changes the character of the function R(T) for Eu_0.7Sr_0.3MnO₃ to metallic (dR/dT>0). For T<T _a and H<H _c a jump in the resistance is observed indicating instability of the electronic state caused by competition between charge and spin ordering of the Mn ions of different valences. Fiz. Tverd. Tela (St. Petersburg) 40, 708–712 (April 1998)     

Diffusion and transport of a magnetic field in a turbulent medium with helicity

An analysis is made of the relation between accurate formulas for the coefficients of turbulent diffusion D _T and the alpha effect α _T for a magnetic field in the Lagrange and Euler representations. It is shown that the quadratic term with respect to α _T in the diffusion coefficient derived by Moffatt and Kraichnan is incorrect and should be dropped. First, a numerical solution of the nonlinear equation (DIA equation) for the Green function is presented, describing the transport of a magnetic field for the case of incompressible, uniform, isotropic, steady-state turbulence possessing helicity. These solutions are used to calculate the steady-state coefficients D _T and α _T for various values of the parameters ξ ₀=u ₀ σ ₀/R ₀, a=H ₀/u ₀ ² p ₀, σ ₀/σ ₁, and R ₀/R ₁, where u ₀, σ ₀, and R ₀ are the characteristic velocity, lifetime, and scale of the turbulent pulsations, and H ₀, σ ₁, and R ₁ are similar values describing the helicity of the medium h(1,2)=〈u(1)· (∇×u(2))〉, and the parameter α characterizes the degree of helicity. The DIA values of D _T and α _T and the self-consistent values of these quantities calculated using the Green tensor in the diffusion approximation are in qualitative agreement. It is shown that the coefficient of turbulent diffusion is always positive for all the types of turbulence studied. Nonsteady-state values of D _T(t) and α _T(t) calculated by a self-consistent method are given. Zh. éksp. Teor. Fiz. 112, 1312–1331 (October 1997)     

Pair tunneling in the low-temperature conductivity of the Cd-Sb alloy high-resistance state near the superconductor-insulator transition

We report a study of the temperature dependence, down to 30 mK, of the magnetoresistance of Cd-Sb alloy in the insulating phase obtained by annealing the quenched metallic superconducting ( _{T c} ≈4.5 K) phase of the alloy. Even though the sample in this state is no longer superconducting, the observed negative magnetoresistance points to single-particle tunneling in the presence of a superconducting gap in the spectrum. At magnetic fields B<T the ratio α(T,B)=R(T,B)/R(T,B=4 T)is found to be maximum at a temperature of about 0.1 K. This behavior indicates a change of the conductivity mechanism from single-particle tunneling to incoherent two-particle tunneling as the temperature decreases. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 10, 713–718 (25 November 1996) Published in English in the original Russian Journal. Edited by Steve Torstveit.     

Influence of magnetic field on the superconducting transition in a Nd1.82Ce0.18CuO4−δ film

The temperature and magnetic-field dependences of the resistivity ρ and Hall effect R(j‖ab, B‖c) in a Nd_1.82Ce_0.18CuO_4−δ single crystal film (T _c =6 K) is investigated at temperatures 1.4≤T≤20 K and magnetic fields 0≤B≤5.5 T. At the lowest temperature T=1.4 K the resistive state (exhibiting resistivity and the Hall effect) arises in a magnetic field B=0.5 T. A transition to the normal state is completed at B _c 2≃3 T, where the Hall coefficient becomes nearly constant. The negative magnetoresistance due to the weak-localization effect in the normal state is observed for B>3 T. The nonmonotonic behavior and the inversion of the sign of R(B) in the mixed state are explained in a reasonable way by the flux-flow model with the effect of pinning taken into account. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 6, 407–411 (25 September 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Influence of transport current and thermal fluctuations on the resistive properties of HTSC+CuO composites

Measurements of the temperature dependence of the electrical resistance R(T) below the superconducting transition temperature have been performed at different values of the transport current in HTSC+CuO composites modeling a network of weak S-I-S Josephson junctions (S—superconductor, I—insulator). It has been shown experimentally that the temperature dependence R(T) at different values of the transport current is adequately described by means of the mechanism of thermally activated phase slippage developed by Ambegaokar and Halperin for tunnel structures. Within the framework of this model we have numerically calculated the temperature dependence of the critical current J _c(T) as defined by various criteria. Qualitative agreement obtains between the measured and calculated temperature dependences J _c(T). Fiz. Tverd. Tela (St. Petersburg) 41, 969–974 (June 1999)     

Morphology of Fractured Polymer‐Polymer Interfaces Bonded at Ambient Temperature as Studied by Atomic Force Microscopy

The amorphous polymer surfaces of polystyrene (PS, M _n=200 kg/mol, M _w/M _n=1.05) and poly(methyl methacrylate) (PMMA, M _n=51.9 kg/mol, M _w/M _n≤1.07) were brought into contact at 21°C to form PS‐PS (for 54 days) and PMMA‐PMMA auto‐adhesive joints (for 11 days). After contact at that temperature corresponding to T _g‐bulk ?81°C for PS and to T _g‐bulk–88°C for PMMA, where T _g‐bulk is the calorimetric glass transition temperature of the bulk sample, the bonded interfaces were fractured and their surfaces were analyzed by atomic force microscopy (AFM). The surface roughness, R _q, of the fractured interfaces was larger by a factor of 3–4 than was that of the free PS and PMMA surfaces aged for the same period of time. A similar increase in R _q was found by comparison of the free PS surface aged at T _g‐bulk+15°C for 1 h and of the surface of the PS‐PS interface fractured after healing at T _g‐bulk+15°C for 1 h. These observations, indicative of the deformation of the fractured interfaces, suggest the occurrence of some mass transfer across the interface even below T _g‐bulk ?80°C.     

From macroscopic to atomic motions in liquid metals

Summary In the present review of liquid dynamics studies on liquid metals are reported. Particularly the case of liquid lead is reviewed because this case was carefully studied by neutron scattering technique,S(Q,ω) being determined at two widely different temperaturesT=623 K andT=1170 K and therefore different densities. In addition extensive supplementary MD simulations were made using a 16 384-particle system. The simulations ranged from a determination of an effective pair potential for lead to simulation of the density correlation functionsF(Q,t) andF _s(Q,t), as well as the longitudinal and transversal current correlation functionsJ ₁(Q,t) andJ _T(Q,t). The MD simulation ?calibrated? via the experimentalS(Q) andS(Q,ω) was used to prolong the range of neutron data to draw conclusions regarding such quantities as dispersion relations for the current correlationsJ ₁(Q,t) andJ _T(Q,t), the generalized viscosity functions ν₁(Q,t), ν₁(Q) and ν_s(Q). Information regarding bulk viscosity ν_B(Q) is also gained. Conclusions are drawn regarding the relative importance of the derived pair potential form by comparison to corresponding hard-sphere data. The general framework of linearized hydrodynamic equations for the macroscopic situation transforming to visco-elastic equations of motion for finite wave-length and high frequency works well also for the case of a continuous potential. The region of transition from simple visco-elastic to hydrodynamic behaviour is occurring at wavelengths in the range (12÷20) ? for the cases studied. The spatial properties of the viscosity functions ν₁(r), ν_s(r) and ν_B(r) are found to correlate well with the range of the radial distribution function for the liquid. The general results for liquid lead probably have wide range of applicability to other simple liquids with similarS(Q) andg(r) properties. The authors have agreed not to receive proofs for correction.     

Lattice Dislocations in a 1-Dimensional Model

The spectral properties of the Schr?dinger operator T(t)=−d ²/dx ²+q(x,t) in L ²(ℝ) are studied, where the potential q is defined by q=p(x+t), x>0, and q=p(x), x<0; p is a 1-periodic potential and t∈ℝ is the dislocation parameter. For each t the absolutely continuous spectrum σ _ac (T(t))=σ _ac (T(0)) consists of intervals, which are separated by the gaps γ _n (T(t))=γ _n (T(0))=(α _n ⁻,α _n ⁺), n≥1. We prove: in each gap γ _n ≠?, n≥ 1 there exist two unique “states” (an eigenvalue and a resonance) λ _n ^±(t) of the dislocation operator, such that λ _n ^±(0)=α _n ^± and the point λ _n ^±(t) runs clockwise around the gap γ _n changing the energy sheet whenever it hits α _n ^±, making n/2 complete revolutions in unit time. On the first sheet λ _n ^±(t) is an eigenvalue and on the second sheet λ _n ^±(t) is a resonance. In general, these motions are not monotonic. There exists a unique state λ₀(t) in the basic gap γ₀(T(t))=γ₀(T(0))=(−∞ ,α₀ ⁺). The asymptotics of λ _n ^±(t) as n→∞ is determined. Received: 5 April 1999 / Accepted: 3 March 2000     

μ+SR Study of Ordering Phenomena in the Heavy-Fermion State of Ce3Pd20Ge6

Magnetic and quadrupolar ordering phenomena in a Ce₃Pd₂₀Ge₆ single crystal have been investigated by muon spin rotation/relaxation (μ⁺SR) spectroscopy. We have observed spontaneous precession of muons in zero-field below T _N =0.7 K in the antiferromagnetic state. The precession frequency follows the power law: ν(T)=ν(0)(1−T/T _N ) ⁿ . The exponent n=0.43(2) is close to the mean-field value of 0.5. The muon longitudinal spin relaxation rate 1/T ₁ is found to be nearly independent of temperature in the range of 0.3 to 2 K, i.e., across either T _N or T _Q =1.2 K, the quadrupolar ordering temperature. Two likely mechanisms for the temperature independent behavior of 1/T ₁ are suggested. This revised version was published online in September 2006 with corrections to the Cover Date.     

Low-temperature anomalies of the Hall coefficient in FeSi

The temperature dependence of the Hall coefficient in the interval 1.8–300 K is investigated in detail in high-quality single-crystal samples of a Kondo insulator — iron monosilicide. It is established that the parameter R _H (T,H=12.5 kOe) changes sign twice in the temperature interval employed, and at temperatures below T _m ≈7 K an anomalous (magnetic) component appears in the angular and field dependences of the Hall voltage. The results of the experimental investigations of R _H (T,H ₀ ) in FeSi are discussed on the basis of the phase diagram in the model of an excitonic insulator. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 10, 774–778 (25 November 1998)     

Metastable Behavior for Bootstrap Percolation on Regular Trees

We examine bootstrap percolation on a regular (b+1)-ary tree with initial law given by Bernoulli(p). The sites are updated according to the usual rule: a vacant site becomes occupied if it has at least θ occupied neighbors, occupied sites remain occupied forever. It is known that, when b>θ≥2, the limiting density q=q(p) of occupied sites exhibits a jump at some p _T=p _T(b,θ)∈(0,1) from q _T:=q(p _T)<1 to q(p)=1 when p>p _T. We investigate the metastable behavior associated with this transition. Explicitly, we pick p=p _T+h with h>0 and show that, as h ↓0, the system lingers around the “critical” state for time order h ^−1/2 and then passes to fully occupied state in time O(1). The law of the entire configuration observed when the occupation density is q∈(q _T,1) converges, as h ↓0, to a well-defined measure.     

Size effects in the melting and crystallization temperatures of copper chloride nanocrystals in glass

The size dependence of the crystallization temperature T _c and melting temperature T _m of copper chloride nanocrystals in glasses is studied in the size range R _a from 1 to 30 nm. Jumps are found in the temperature dependence of T _c at R _a =13 nm and R _a =1.8 nm, a jump is found in the temperature dependence of T _m at R _a =2.2 nm, and the supercooling of the melt is found to vanish in the case of crystallization at R _a ⩽1.4 nm. It is conjectured that the jump in T _c with large R _a occurs for a nano-crystal radius equal to that of a crystalline nucleus in the melt, and the jumps in T _c and T _m for smaller values of R _a are due to a change in the shape (faceting) of the nanocrystals. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 7, 481–486 (10 October 1997)     

Excitations in Heisenberg spin glasses

Within the RPA approach forT=0, the excitations of the Heisenberg spin glass system Eu _x Sr_1–x S are studied by numerical methods, using a continued fraction algorithm. Both the density of statesg(E) and also the spectral functionS(q,E) are calculated for systems with (16)³ sites, withx=0.4, 0.5, and 0.6 (spin glass phase), and also forx0.7 (ferromagnetic phase). Forq-vectors within the (1,1,1) plane,S(q,E) shows magnon peaks even in the spin glass phase, over the whole range ofq. However, these peaks are quite broad, and there is considerable intensity at small energies even for largeq, leading to a finite intercept ofg(E) forE0. Over a large temperature range, the specific heat is approximately linear inT forx0.7.     

Temperature behavior of conductivity in a La2CuO4 + δ single crystal upon the paramagnetic-antiferromagnetic transition

The temperature dependence of the resistance of a La₂CuO_{4 + δ} (δ ≈ 0.05) single crystal with the Neel temperature T _N ≈ 205 K was investigated in order to establish the correlation between the transport and magnetic properties of the crystal. The R(T) dependence near T _N reveals a kink related to the enhancement of sample’s conductivity upon the transition from the antiferromagnetic to paramagnetic state. With an increase in temperature far above T _N, the transition from the dielectric (dR/dT < 0) to metal (dR/dT > 0) occurs. The observed behavior of resistance is attributed to delocalization of carriers above T _N.     

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)     

Characteristic features of the temperature dependence of the surface impedance of YBa2Cu3O6.95 single crystals

The real and imaginary parts of the surface impedance Z _s =R _s +iX _s of YBa₂Cu₃O_6.95 single crystals are measured at a frequency ω/π=9.4 GHz. The quantities R _s (T) and X _s (T) are linear functions of temperature for T<0.3T _c (T _c =93.5 K). A maximum of R _s (T) and a plateau of X _s (T) are observed in the interval 35<T<65 K. Our experimental data, just as all recent measurements of R _s (T) in YBa₂Cu₃O_6.95 single crystals in the temperature range 0<T<1.3T _c , are described well in a two-fluid model which assumes electron-phonon scattering of quasiparticles. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 12, 893–898 (25 June 1997)     

Magnetic field dependence ofT c and temperature dependence ofH c2 in layered superconductors with open normal state Fermi surface

A theoretical framework for treating the effects of magnetic fieldH on the pairing theory of superconductivity is considered, where the field is taken in an arbitrary direction with respect to crystal axes. This is applicable to closed, as well as open normal state Fermi surface (FS), including simple layered metals. The orbital effects of the magnetic field are treated semiclassically while retaining the full anisotropic paramagnetic contribution. Explicit calculations are presented in the limits |H| → |H _c2(T)|,T ∼ 0 andT →T _c(|H|), |H| ∼ 0. Effects of weak nonmagnetic impurity scattering, without vertex corrections, have also been taken into account in a phenomenological way. The final results for the case of open FS and layered materials are found to differ considerably from those of the closed FS. For example, an important parameter,h(T=0)=|H_c2(0)|/[-Tδ|H _c2 T|δT]_T{s0} for the case of a FS open ink _z-direction with thek _z-bandwidth, 4t ₃, very small compared to the Fermi energy,E _F, is close to 0.5906, compared to 0.7273 for the closed FS, in the clean limit. Analytical results are given for the magnetic field dependence ofT _c and the temperature dependence of H _c2 for a model of layered superconductors with widely open FS. For a set of band structure parameters for YBa₂Cu₃O₇ used elsewhere, we find reasonable values for the upper critical fieldH _c2(0), the slope (dH _c2/dT)_{T c0}, anisotropic coherence lengths ζ_i(T=0),i=x, y, z, and (dT _c/d|H|)_{|H| → 0}.     

ESR millimeter-band spectroscopy of magnetic ordering in the low-dimensional magnet CuGeO3

Resonant absorption of microwaves in CuGeO₃ single crystals in a frequency band of 40 to 120 GHz, in magnetic field B⩽15 T, at temperatures ranging between 0.5 and 300 K, and in the configuration B∥a has been investigated. Several absorption lines (S ₀, S _a, and S _b) whose parameters strongly depend on temperature have been detected close to ESR. The temperature dependence of the total absorption in the main line S ₀ with the Landé g-factor g ₀=2.154 at temperatures above the spin-Peierls transition temperature is in good agreement with Bonner and Fisher’s theoretical prediction for a one-dimensional Heisenberg spin chain. In addition to the main resonance, a resonance of smaller amplitude, S _a, with the g-factor g _a=2.72 has been detected at temperatures ranging down to a characteristic temperature T≃1 K, below which the amplitude of this feature drops to zero. A radical restructuring of the magnetoabsorption spectrum occurs at the temperature of the spin-Peierls transition T _SP≈14 K. At T<12 K new features emerge in the spectrum, namely, a broad absorption line overlapping with the narrow lines S ₀ and S _a, and a line S _b with g _b=1.83, which is not detected at temperatures above T _SP. An analysis of amplitudes and total absorption of ESR lines as functions of temperature has shown that the temperature range below 1 K is anomalous, which may be caused by an additional ordering in the CuGeO₃ magnetic subsystem at low temperatures. Zh. éksp. Teor. Fiz. 112, 1727–1738 (November 1997)