Level statistics inside the core of a superconductive vortex

A microscopic theory of the Efetov supermatrix sigma-model type is constructed for the low-lying electron states in a mixed superconductive-normal system with disorder. This technique is used for the study of the localized states in the core of a vortex in a moderately clean superconductor with τ ⁻¹≫ω ₀∼Δ²/E _F . At low energies ε≪ω _Th∼ (ω ₀/τ)^1/2, the energy level statistics is described by the “zero-dimensional” limit of this supermatrix theory, and the result for the density of states is equivalent to that obtained within Altland-Zirnbauer random matrix model. Nonzero modes of the sigma model increase the mean interlevel distance by the relative amount [2 ln (1/ω ₀ τ)]⁻¹. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 78–83 (10 July 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Numerical study of the directed polymer in a 1 + 3 dimensional random medium

The directed polymer in a 1+3 dimensional random medium is known to present a disorder-induced phase transition. For a polymer of length L, the high temperature phase is characterized by a diffusive behavior for the end-point displacement R² ∼L and by free-energy fluctuations of order ΔF(L) ∼O(1). The low-temperature phase is characterized by an anomalous wandering exponent R²/L ∼L^ω and by free-energy fluctuations of order ΔF(L) ∼L^ω where ω∼0.18. In this paper, we first study the scaling behavior of various properties to localize the critical temperature T_c. Our results concerning R²/L and ΔF(L) point towards 0.76 < T_c ≤T₂=0.79, so our conclusion is that T_c is equal or very close to the upper bound T₂ derived by Derrida and coworkers (T₂ corresponds to the temperature above which the ratio remains finite as L ↦ ∞). We then present histograms for the free-energy, energy and entropy over disorder samples. For T ≫T_c, the free-energy distribution is found to be Gaussian. For T ≪T_c, the free-energy distribution coincides with the ground state energy distribution, in agreement with the zero-temperature fixed point picture. Moreover the entropy fluctuations are of order ΔS ∼L^1/2 and follow a Gaussian distribution, in agreement with the droplet predictions, where the free-energy term ΔF ∼L^ω is a near cancellation of energy and entropy contributions of order L^1/2.     

Logarithmic temperature dependence of the conductivity of the two-dimensional metal

We report on the first observation and studies of a weak delocalizing logarithmic temperature dependence of the conductivity, which causes the conductivity of the 2D metal to increase as T decreases down to 16 mK. The prefactor of the logarithmic dependence is found to decrease gradually with density, to vanish at a critical density n _c , 2∼2×10¹² cm⁻², and then to have the opposite sign at n>n _c ,2. The second critical density sets the upper limit on the existence region of the 2D metal, whereas the conductivity at the critical point, G _c ,2∼120e ²/h, sets an upper (low-temperature) limit on its conductivity. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 497–501 (25 September 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Reciprocity relations for the effective electrical conductivity of randomly inhomogeneous media in the fractal regime

An exact relation for the realization-averaged effective conductivities in the fractal region is found for two-dimensional randomly inhomogeneous media. It has the form {σ _e (τ,L)~× {1/σ _e (−τ,L)~⁻¹=σ _e ² (τ=0, L≫ξ), where ξ is the correlation length (the self-averaging scale), L is the size of the system, τ=(p-p _c )/p _c , and p _c is the percolation threshold. For L≫ ξ, the system is self-averaged, and the relation transforms into the Dykhne reciprocity relation, A. M. Dykhne, Zh. éksp. Teor. Fiz. 59, 110 (1970) [Sov. Phys. JETP 32, 63 (1971)] σ _e (τ)σ _e (−τ])=σ _e ² (τ=0)= σ ₁ σ ₂. A similar relation is obtained for media with an exponentially broad distribution of local conductivities, as well as for individual realizations of some deterministic structures. Zh. éksp. Teor. Fiz. 113, 1484–1490 (April 1998)     

Anisotropic impurity scattering in palladium silver alloys

Measurements have been made of the Hall coefficientR of some alloys of silver in palladium over the temperature range 1°K to 120°K. The alloys contain between ∼1 and ∼10 at.-% silver. Values ofR were also obtained at room temperature and these were in good agreement with earlier published work. The values ofR are negative in all the alloys, and |R| increases both on reducing the temperature and increasing the silver concentration,c. Below ∼10°K, |R| becomes independent of temperature but shows a linear dependence onc, increasing by a factor of 2.5 over the concentration range measured. This increase is too great to be accounted for in terms of band structure changes alone, so we have examined the effects of anisotropic impurity scattering. To a first approximation it can be shown thatR is proportional to an anisotropy parameterA, defined asA=〈τ ²(k)〉/〈τ(k)〉², whereτ(k) represents the relaxation time of an electron in a statek, and 〈〉 is an average over the Fermi surface. In palladium we assume that the majority of the current is carried by the s-electrons. In the presence of silver impurities these electrons can be scattered into s-states or d-states with relaxation times given byτ _ss α1/c(1−c) andτ _sd α1/c ²(1−c) respectively. FollowingPlate we have assumed thatτ _ss is isotropic and thatτ _sd is anisotropic, leading to an overall anisotropic relaxation time for impurity scattering. We then find the parameterA increases approximately linearly with silver content, in accordance with our experimental results.     

Submillimetric cyclotron resonance linewidths and electron relaxation time in copper

For the first time submillimetric microwaves (λ<1 mm) are used to observe Azbel' Kaner cyclotron resonance in metals. The very high frequency used (typicallyF≅400 GHz) gives a large value ofωτ (typically 500) and therefore very sharp peaks. The fundamental resonance fieldH _c=m ^* cω/e is rather high (typically 200 KG), so subharmonicsH _c/n can be observed at many values ofH in the field region 0–27 KG. If relatively few electrons participate in the resonance and ifω _cτ≧50 (ω _c=eH/m ^* c,τ relaxation time) thenChambers has shown that the line shapes are independent of relaxation time while the fractional linewidthΔH/H varies as l/ωτ. For the belly orbit in pure copper the conditions of Chambers' theory are satisfied forH≧20 KG parallel to [111] axis.m ^* is a minimum andτ=1.8×10⁻¹⁰ s.     

Breakdown of the linear current regime in periodic structures

We study the effect of a weak nonlinearity in media on the linear regime of current flow in two-dimensional periodic structures with two equal component concentrations. We find that the asymptotic behavior of the electric field and current as functions of the distance between the angles in heterogeneous media is determined by the parameter h=σ ₂/σ ₁ (here σ ₁ and σ ₂ are the linear conductivities of the cells) and the external magnetic field B. This dependence leads to divergence of the higher-order moments of field and current at certain critical values h _c and B _c and to divergence of the response functions related to the higher-order moments. For square cells the effective nonlinear conductivity diverges at h⩽h _c, with . For structures of general shape we find the dependence of h _c on the angles and the external magnetic field. We show that for a given structure the linear regime of current flow in the system can be reversibly transformed into a nonlinear one by varying the magnetic field strength. The critical field B _c is approximately determined from the condition ω _c τ∼1, where ω _c and τ ⁻¹ are, respectively, the cyclotron frequency and the collision rate. Finally, we discuss the feasibility of detecting these effects experimentally. Zh. éksp. Teor. Fiz. 112, 643–660 (August 1997)     

Critical currents in polycrystalline thin films of high-T c superconductors

Summary It is shown that the behaviour of the temperature dependence of the critical current in polycrystalline thin films of high-T _c superconductors depends crucially on the assumption made concerning the nature of the intergranular material. The usual assumption of a superconductor-insulator-superconductor (=SIS) ?sandwich? between each grain leads to a crossover fromI _c∼(1−T/T _c) toI _c∼(1−T/T _c)^3/2, for temperatures nearT _c (whereI _c is the critical current,T the absolute temperature, andT _c the superconducting transition temperature). Instead, for a superconductor-normal metal-superconductor (=SNS) sandwich the dependenceI _c∼(1−T/T _c)² is found for all temperatures. Consideration is given to the effect of self-magnetic field on the analysis. The comparison between expressions for continuous and granular systems is extended. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction.     

On the investigation of magnetic critical phenomena in ferromagnets by μSR and PAC

On the basis of current theoretical views on the critical phenomena in isotropic Heisenberg ferromagnets the power temperature behavior Λ=c(τ)λ₀τ^-w has been derived for the muon spin relaxation rate Λ as π-T _c ⁻¹ (T-T _c ) → 0⁺. It is shown that the crossover from an exchange critical regime to a dipolar one is accompanied not only with the change in the critical exponentw in the above law, but also with the reduction of the coefficientc(π). A comparison with the temperature behaviour of the inverse nuclear relaxation timet _R ⁻¹ measured in the PAC experiment is carried out.     

On the phase boundaries of the integer quantum Hall effect. Part II

It has been shown that the observation of the transitions between the dielectric phase and the integer-quantum-Hall-effect phases with the quantized Hall conductivity σ _xy ^q ≥ 3e ²/h announced in a number of works is unjustified. In these works, the crossing points of the magnetic-field dependence of the diagonal resistivity ρ _xx at different temperatures T and ω_cτ = 1 have been misidentified as the critical points of the phase transitions. In fact, these crossing points are due to the sign change of the derivative dρ _xx /dT owing to the quantum corrections to the conductivity. Here, ω_c = eB/m is the cyclotron frequency, τ is the transport relaxation time, and m is the effective electron mass.     

Possible manifestation of spin fluctuations in the temperature behavior of the resistivity of Sm<Subscript>1.85</Subscript>Ce<Subscript>0.15</Subscript>CuO<Subscript>4</Subscript> thin films

A pronounced step-like (kink) behavior in the temperature dependence of resistivity ρ(T) is observed in the optimally doped Sm_1.85Ce_0.15CuO₄ thin films around T _sf = 87 K and attributed to the manifestation of strong-spin fluctuations induced by Sm³⁺ moments with the energy ħω_sf = k _B T _sf ≃ 7 meV. The experimental data are found to be well fitted by the residual (zero-temperature) ρ_res, electron-phonon ρ_e-ph(T) = AT, and electron-electron ρ_e-e(T) = BT ² contributions in addition to the fluctuation-induced contribution ρ_sf(T) due to thermal broadening effects (of the width ω_sf). According to the best fit, the plasmon frequency, impurity scattering rate, electron-phonon coupling constant, and Fermi energy are estimated as ω_p = 2.1 meV, τ ₀ ⁻¹ = 9.5 × 10⁻¹⁴ s⁻¹, λ = 1.2, and E _F = 0.2 eV, respectively. The text was submitted by the authors in English.     

Short-circuit current limiter utilizing a high-Tc superconductor

Experimental data are given on a prototype short-circuit current limiter utilizing a polycrystalline high-T _c superconductor of composition Y₁Ba₂Cu₃O_7−δ . The limiter comprises a seriesconnected dc circuit element immersed in liquid nitrogen. To improve the efficiency, a polycrystalline high-T _c superconductor having an S-shaped current-voltage characteristic is used as the current limiter. Zh. Tekh. Fiz. 68, 129–130 (October 1998)     

Generalized Ginzburg-Landau equation and the properties of superconductors with Ginzburg-Landau parameter κ close to 1

An expression is derived for the free energy of a superconductor near the critical temperature, taking account of the terms of next highest order in the parameter 1−T/T _c. These terms become important for Ginzburg-Landau parameter values |κ−1|≪1, and in this case, in an external magnetic field H ₀ close to H _c2, the structure of the order parameter is determined by the relative values of the three small parameters |κ−1|, 1−T/T _c, and (H _c2−H ₀)/H _c2. Three types of lattices are investigated: triangular with one and two flux quanta per cell and square with one flux quantum per cell. Zh. éksp. Teor. Fiz. 115, 726–739 (February 1999)     

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)     

Decay of an electronic vortex of a collisionless shock wave as a possible mechanism of a “Coulomb explosion”

A new mechanism of a “Coulomb explosion,” where ions are accelerated by the electric field separating charges at the magnetic Debye radius r _B∼B/4πen _e, is proposed on the basis of a nonquasineutral model of electronic vortices in a magnetic field. It is shown by means of numerical calculations that in the process of acceleration of the ions a collisionless shock wave, whose front has an effective width of the order of δ∼r _B, determined by the breakdown of quasineutrality, is formed in a time of the order of ω _pi ⁻¹ , where ω_pi is the ion plasma frequency. The origin of such explosive dynamics is the formation of “holes” in the electron density at characteristic times of the order of ω _pe ⁻¹ (ω_pe is the electronic plasma frequency) as a result of the generation of electronic vorticity by the Weibel instability of an electromagnetic wave. Calculations for a laser pulse with intensity J∼6×10¹⁸ W/cm² show that the ions expand in the radial direction with velocities up to 3.5×10⁸ cm/s. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 10, 669–674 (25 November 1999)     

Plasma parameters in the upgraded Trimyx-M Galathea

Results are presented from measurements of the plasma parameters in the upgraded Trimyx-M Galathea. After the barrier magnetic field and the energy of the injected hydrogen plasma bunch were increased to B _bar ∼ 0.1 T and W ₀ ≈ 200 J, respectively, the following plasma parameters were achieved: the density n ∼ 5 × 10¹³ cm⁻³, the plasma confinement time τ* = 800–900 μs, the elergy of the confined plasma W ₁ ∼ 100 J, the ratio of the plasma pressure to the barrier magnetic pressure β ₀ ∼ 0.2, the electron temperature T _e ∼ 20 eV, and the ion temperature T _i ∼ 2T _e . The maximum time during which the plasma density decreased e-fold, τ _p , was found to be 300 μs at B _bar = 0.1 T, which agrees with the classical transport model.     

Study of the magnetic state of a highly dispersed BaO · 6Fe2O3 system with near-critical particle size

An investigation was made of the magnetic state of a system of highly anisotropic BaO · 6Fe₂O₃ nanocrystals several lattice parameters thick and having a near-critical volume (∼10⁻¹⁸ cm³), obtained using cryochemical technology. It is observed that the particles are transformed to the superparamagnetic state and it is shown that the external magnetic field plays a role in its formation. An H-T diagram was obtained for the temperature range 300 K-T _c, which shows various regions uncharacteristic of the macro-object, which are specifically attributed to the distribution over the anisotropy fields in the system and the impaired magnetic structure in the surface zone of the particles. Relatively large regions of magnetic fields and temperatures were observed where reversible rotation of the magnetization vector of particles with near-critical volume plays an important role. Fiz. Tverd. Tela (St. Petersburg) 40, 1294–1297 (July 1998)     

Electron transport in hybrid superconductor heterostructures with manganite interlayers

Hybrid herostructures comprising an YBa₂Cu₃O _x (YBCO) high-temperature superconductor (HTS) layer and Nb/Au low-temperature superconductor (LTS) bilayer (with critical HTS and LTS temperatures T _c and T′_c, respectively), separated by a thin (d _M = 5–20 nm) interlayer of LaMnO₃, La_0.7Ca_0.3MnO₃, or La_0.7Sr_0.3MnO₃ manganite have been studied. The electric resistance and magnetic properties of individual (evaporated directly onto the substrate) manganite films and related hybrid herostructures have been measured. Based on quasi-classical equations, analytical expressions for the conductivity of herostructures at T ≤ T′_c are obtained in the case of a low-transparency superconductor/manganite interface. It is established that the conductivity of heterostructures is determined by the proximity effect (related to the penetration of a condensate wavefunction from the Nb/Au bilayer to manganite) and depends strongly on interface transparency. At low temperatures (T ≪ T _c′), the conductivity peaks are found at voltages determined by the exchange field of the manganite interlayer. At T _c′ < T < T _c, conductivity features at nearly zero bias voltages are observed, which are related to the superconductivity of the YBCO electrode.     

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)     

Normal-metal hot-electron bolometer with Andreev reflection from superconductor boundaries

This paper describes the design and experimental testing of a high-sensitivity hot-electron bolometer based a film of normal metal, exploiting the Andreev reflection from superconductor boundaries, and cooled with the help of a superconductor-insulator-normal metal junction. At the measured thermal conductivity, G≈6×10⁻¹² W/K, and a time constant of τ=0.2 μs, and a temperature of 300 mK, the estimated noise-equivalent power NEP=5×10⁻¹⁸ W/Hz^1/2, assuming that temperature fluctuations are the major source of noise. At a temperature of 100 mK, the thermal conductivity drops to G≈7×10⁻¹⁴ W/K, which yields NEP=2×10⁻¹⁹ W/Hz^1/2 at a time constant of τ=5 μs. The microbolometer has been designed to serve as a detector of millimeter and FIR waves in space-based radio telescopes. Zh. éksp. Teor. Fiz. 115, 1085–1092 (March 1999)