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 ).     

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.     

Phase diagram and transport properties of Sb-doped Ca0.88La0.12Fe2As2 single crystals

The effects of isovalent Sb substitution on the superconducting properties of the Ca_0.88La_0.12Fe₂(As_1-ySb_y)₂ system have been studied through electrical resistivity measurements. It is seen that the antiferromagnetic or structural transition is suppressed with Sb content, and a high-T_c superconducting phase, accompanied by a low-T_c phase, emerges at 0.02 ≤ y ≤ 0.06. In this intermediate-doping regime, normal-state transport shows non-Fermi-liquid-like behaviors with nearly T-linear resistivity above the high-T_c phase. With further Sb doping, this high-T_c phase abruptly vanishes for y > 0.06 and the conventional Fermi liquid is restored, while the low-T_c phase remains robust against Sb impurities. The coincidence of the high-T_c phase and non-Fermi liquid transport behaviors in the intermediate Sb-doping regime suggests that AFM fluctuations play an important role in the observed non-Fermi liquid behaviors, which may be intimately related to the unusual nonbulk high-T_c phase in this system.     

Variable-range cotunneling and conductivity of a granular metal

The Efros-Shklovskii (E-S) law for the conductivity of granular metals is interpreted as a result of a variable-range cotunneling process. The cotunneling between distant resonant grains is predominantly elastic at low T ≤ T _c , while it is inelastic (i.e., accompanied by creation of electron-hole pairs on a string of intermediate non-resonant grains) at T ≥ T _c . The corresponding E-S temperature T _ES , in the latter case, is slightly (logarithmically) T dependent. The magnetoresistance in the two cases is different: it may be relatively strong and negative at T?T _c , while, at T > T _c , it is suppressed due to inelastic processes, which destroy the interference.     

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.     

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 .     

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 \(\sqrt {{{T_c } \mathord{\left/ {\vphantom {{T_c } {T - T_c }}} \right. \kern-\nulldelimiterspace} {T - T_c }}} \).     

Electron transport,penetration depth,and the upper critical magnetic field in ZrB<Subscript>12</Subscript> and MgB<Subscript>2</Subscript>

We report on the synthesis and measurements of the temperature dependences of the resistivity ρ, the penetration depth λ, and the upper critical magnetic field H_c2, for polycrystalline samples of dodecaboride ZrB₁₂ and diboride MgB₂. We conclude that ZrB₁₂ behaves as a simple metal in the normal state with the usual Bloch-Grüneisen temperature dependence of ρ(T) and with a rather low resistive Debye temperature T_R = 280 K (to be compared to T_R = 900 K for MgB₂). The ρ(T) and λ(T) dependences for these samples reveal a superconducting transition in ZrB₁₂ at T_c = 6.0 K. Although a clear exponential λ(T) dependence in MgB₂ thin films and ceramic pellets was observed at low temperatures, this dependence was almost linear for ZrB₁₂ below T_c/2. These features indicate an s-wave pairing state in MgB₂, whereas a d-wave pairing state is possible in ZrB₁₂. In disagreement with conventional theories, we found a linear temperature dependence, of H_c2(T) for ZrB₁₂ (H_c2(0) = 0.15 T).     

Mechanism of carrier generation and the origin of the pseudogap and 60 K phases in YBCO

The mechanism of hole carrier generation is considered in the framework of a model assuming the formation of negative U centers (NUCs) in HTSC materials under doping. The calculated dependences of carrier concentration on the doping level and temperature are in quantitative agreement with experiment. An explanation is proposed for the pseudogap and 60 K phases in YBa₂Cu₃O_6+δ. It is assumed that a pseudogap is of superconducting origin and arises at temperature T* > T_c∞ > T_c in small nonpercolating clusters as a result of strong fluctuations in the occupancy of NUCs (T_c∞ and T_c are the superconducting transition temperatures of an infinitely large and finite NUC clusters, respectively). The T*(δ) and T_c(δ) dependences calculated for YBa₂Cu₃O_6+δ correlate with experimental dependences. In accordance with the model, the region between T*(δ) and T_c(δ) is the range of fluctuations in which finite nonpercolation clusters fluctuate between the superconducting and normal states due to NUC occupancy fluctuations.     

On the effect of heating and cooling rates on the melting and crystallization of metal nanoclusters

The effect of heating and cooling rates on melting (T_m) and crystallization (T_c) temperatures of metal nanoclusters is investigated in terms of the isothermal molecular dynamics. We report on the results obtained for nickel nanoclusters, although analogous results were also obtained for gold and aluminum nanoclusters. It is found that T_m increases, while T_c decreases with increasing heating and cooling rates, both T_m and T_c tending to the same value for heating and cooling rates tending to zero. The results indicate that the hysteresis of melting and crystallization of nanoparticles must be completely due to nonequilibrium conditions of heating and cooling. The transition of Ni nanoclusters to the amorphous state begins at very high cooling rates exceeding 10 TK/s.     

Low-temperature anomalies in the specific heat and thermal conductivity of MgB<Subscript>2</Subscript>

The temperature dependences of the specific heat C(T) and thermal conductivity K(T) of MgB₂ were measured at low temperatures and in the neighborhood of T _c . In addition to the well-known superconducting transition at T _c ≈40 K, this compound was found to exhibit anomalous behavior of both the specific heat and thermal conductivity at lower temperatures, T≈10–12 K. Note that the anomalous behavior of C(T) and K(T) is observed in the same temperature region where MgB₂ was found to undergo negative thermal expansion. All the observed low-temperature anomalies are assigned to the existence in MgB₂ of a second group of carriers and its transition to the superconducting state at T_c2≈10?12 K.     

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.     

Heat capacity anomaly in the vicinity of the tricritical and upper critical points

The anomalous behavior of the isochoric heat capacity of a mixture of methane, pentane and heptane is studied experimentally in the vicinity of the liquid-vapor critical point in the cases when (a) the critical temperature T _c approaches the tricritical point T _TCP and (b) the critical temperature approaches the upper critical end point T _U . It is shown that in all cases, the singular part of the heat capacity of the mixture has the form C_sing=A¦τ¦^?α, where τ=(T ? T _c )/T _c and α≈0.11. When T _c →T _U , amplitude A of the heat capacity anomaly is found to be approximately constant. At the same time, the amplitude of the anomaly tends to zero in the vicinity of the tricritical point: A∝¦τ_c¦^ε, where τ_c=(T _c ? T _TCP )/T _TCP and ε=1.6?1.7. The inevitable vanishing of this mode of the heat capacity anomaly leads to a negative value of the critical index \(\tilde \alpha\) characterizing the heat capacity anomaly at the tricritical point, while the tricritical point theory and the isomorphism hypothesis predict \(\tilde \alpha = 0.5\).     

X-ray study of [N(CH<Subscript>3</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>ZnCl<Subscript>4</Subscript> at low temperatures

The unit cell parameters a, b, and c of [N(CH₃)₄]₂ZnCl₄ have been measured by x-ray diffraction in the temperature range 80–293 K. Temperature dependences of the thermal expansion coefficients α_a, α_b, and α_c along the principal crystallographic axes and of the unit cell thermal expansion coefficient α_V were determined. It is shown that the a=f(T), b=f(T), and c=f(T) curves exhibit anomalies in the form of jumps at phase transition temperatures T₁=161 K and T₂=181 K and that the phase transition occurring at T₃=276 K manifests itself in the a=f(T) and b=f(T) curves as a break. A slight anisotropy in the coefficient of thermal expansion of the crystal was revealed. The phase transitions occurring at T₁=161 K and T₂=181 K in [N(CH₃)₄]₂ZnCl₄ were established to be first-order.     

Anomalous temperature dependence of magnetic relaxation in YBa<Subscript>2</Subscript>Cu<Subscript>2</Subscript>O<Subscript>7 − δ</Subscript> oxygen-deficient single crystals

The dependence of the magnetization relaxation rate S = ?d lnM/dlnt on temperature T is measured in YBa₂Cu₃O_{7 ? δ} samples with various oxygen concentrations. It is found that the S(T) curve changes qualitatively when oxygen deficit δ exceeds the threshold value δ_th = 0.37. For δ < δ_th (T _c > 60 K, where T _c is the superconducting transition temperature), function S(T) has the well-known peak at T/T _c = 0.4. For δ > δ_th (at T _c < 51 K), this peak transforms into a plateau and a new sharp peak appears at T/T _c = 0.1. The threshold value δ_th of the oxygen deficit corresponds to the transition of the sample from the disordered state into the ordered state of oxygen vacancies. We consider the change in the shape of the S(T) curve as a macroscopic manifestation of this transition.     

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.     

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).     

A new critical point in the non-linear conductivity due to variable range hopping in Si

A critical point in the non-linear conductivity has been observed in epitaxial silicon in the variable range hopping regime, due to a negative differential resistance with a dc bias currentI _dc. This gives thermal breakdown via the electron-phonon coupling and circuit-limited oscillations with a frequencyf∝I _dc, below a critical temperatureT _c. This critical behaviour is intrinsic, and forR(T)=R ₀ exp(T ₀ /T)^1/2 we show thatT _c=0.00512T ₀.     

Anisotropy of microwave conductivity in the superconducting and normal states of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7</Subscript>−<Emphasis Type="Italic">x</Emphasis>: 3D-2D crossover

The imaginary parts of microwave conductivity σ″(T<T_c) and resistivity ρ (_T)=1/σ(T>T_c) along (σ _ab ^″ and ρ_ab) and across and (σ _c ^″ and ρ_c the cuprate ab planes of a YBa₂Cu₃O_7?x crystal with the oxygen doping level x varying from 0.07 to 0.47 were measured in the temperature range 5≤ T≤200 K. In the superconducting state, the σ _ab ^″ (T)/σ _ab ^″ (0) and σ _c ^″ (T/σ _c ^″ (0) curves coincide for an optimally doped (x=0.07) crystal, but, with an increase in x, the slopes of the σ _c ^″ (T)/σ _c ^″ (0) curves decrease noticeably at T<T_c/3, on the background of small changes happening to the σ _ab ^″ (T/σ _ab ^″ (0) curves. The two-dimensional (2D) transport along the ab planes in the normal state of YBa₂Cu₃O_7?x is always metallic, but there is a crossover (at x=0.07) from the Drude to hopping (at x>0.07) conductivity along the c axis. This is confirmed both by the estimates of the lowest metallic and the highest tunneling conductivities along the c axis and by quantitative comparison of the measured ρ_c(T) curves with the curves calculated in the polaron model of quasiparticle transport along the c axis.     

Size effects in electrical and magnetic properties of quasi-one-dimensional tin wires in asbestos

Bulk composites have been prepared based on one-dimensional fibers of natural chrisothil-asbestos with various internal diameters (d = 6–2.5 nm) filled with tin. The electrical and magnetic properties of quasi-one-dimensional Sn wires have been studied at low temperatures. The electrical properties have been measured at T = 300 K at a pressure P = 10 kbar. It has been found that the superconducting (SC) characteristics of the nanocomposites (critical temperature T_c and critical magnetic field H_c) increase as the Sn filament diameter decreases. The temperature spreading of the resistive SC transition also increases as the Sn filament diameter decreases, which is explained by the SC order parameter fluctuations. The size effects (the increase in critical temperature T_c and transition width ΔT_c) in Sn nanofilaments are well described by the independent Aslamazov–Larkin and Langer–Ambegaokara fluctuation theories, which makes it possible to find the dependence of T_c of the diffuse SC transition on the nanowire diameter. Using the temperature and magnetic-field dependences of the magnetic moment M(T, H), it has been found that the superconductor–normal metal phase diagram of the Sn–asbestos nanocomposite has a wider region of the SC state in T and H as compared to the data for bulk Sn. The magnetic properties of chrisotil-asbestos fibers unfilled with Sn have been studied. It has been found that the Curie law is fulfilled and that the superparamagnetism is absent in such samples. The obtained results indicate the absence of magnetically ordered impurities (magnetite) in the chrisotil-asbestos matrix, which allowed one to not consider the problem of the interaction of the magnetic subsystem of the asbestos matrix and the superconducting subsystem of Sn nanowires.