Nuclear spin-lattice relaxation in the mixed state of superconducting niobium

Pulsed NMR measurements of the spin-lattice relaxation timeT ₁ have been carried out in niobium metal, in order to investigate the elementary excitation spectrum in the superconducting mixed state. The dependences ofT ₁ on temperature, external field, and mean free path were determined. The results below ～5°K were in agreement with the theory of field-induced gapless superconductivity. The best fit was obtained with a scale factor 0.35±0.2, in agreement with recent ultrasonic attenuation results. Anomalously fast relaxation was observed above ～5°K, which could not be interpreted in terms of the present theory of thermal vortex fluctuations.     

Surface induced mixed state of a superconducting film

Presented in this paper is a theoretical analysis of a planar surface induced mixed state for a superconducting film in parallel applied field. An analytical solution of the internal magnetic field is obtained based on Saint-James and de Gennes' order parameter in a film. An expression of Gibbs free energy per unit volume without restriction of a geometry is derived from non-linear Ginzburg-Landau (GL) equation in terms of a renormalized GL parameter and a modified geometric factor. Based on the Gibbs free energy, a phase diagram of distinguishing a first and second order phase transition for a type I superconducting film is calculated. The numerical results for exact solutions of spatial variation of order parameter, current density and internal magnetic field in the film geometry in parallel applied field case are presented. Near the upper critical field, the first entry of an applied field in the film exhibits a laminar structure.     

Temperature dependence of the magnetization in the mixed state of superconducting alloys

The theory of Abrikosov of the immediate subcritical region in the mixed state is extended by means of the generalized Ginzburg-Landau theory to temperatures belowT _c and arbitrary mean free pathl of the electrons. The results for the magnetization and the free energy can still be presented in the form derived by Abrikosov apart from the fact thatκ is replaced by a new parameterκ ₂(T). The slope of the curveκ ₂/κ versust=T/T _c att=1 is found to decrease monotonically from ?0.105 to — (1.367-0.136κ ^?2) asl increases from zero to infinity. The results for short mean free paths are consistent with experiment, in particular,κ ₂ is always larger thanκ in the vicinity ofT _c . But the experimental temperature dependence ofκ ₂/κ in pure Nb is much higher than the theoretical one.     

Scaling of ac susceptibility and the nonlinear response function of high-temperature superconductors

The amplitude-dependent ac susceptibility of high-temperature superconductors is shown to obey some empirical scaling relations. We try to analyze this behavior by extending a dc nonlinear response function of mixed state to the ac cases. The derived equations for critical current and ac susceptibility X(T) agree with the scaling relations of experimental data.     

Unusual magnetic-field-induced phase transition in the mixed state of superconducting NbSe2

The thermal conductivity kappa in the basal plane of single-crystalline hexagonal NbSe2 has been measured as a function of magnetic field H, oriented both along and perpendicular to the c axis, at several temperatures below T(c). With the magnetic field in the basal plane and oriented parallel to the heat flux we observed, in fields well below H(c2), an unexpected hysteretic behavior of kappa(H) with all the generic features of a first order phase transition. The transition is not manifest in the kappa(H) curves, if H is still in the basal plane but oriented perpendicularly to the heat-flux direction. The origin of the transition is not yet understood.     

Measurements of the low temperature heat capacity of niobium in the superconducting mixed state

Low temperature measurements of the heat capacity of niobium in the mixed state obtained at constant magnetic induction are presented, and are compared with the heat capacity expected form electronic excitations bound to the cores of individual flux lines. The formation of the intermediate mixed state is shown to have a pronounced influence on measurements at elevated temperatures and complicates comparison with theory at low temperatures. Our measurements are qualitatively consistent with the reduction in core size with decreasing temperature recently predicted by Kramer and Pesch.     

The superconducting transition and the behavior of the ac susceptibility

The ac susceptibility behavior of superconductors close to the superconducting transition temperature is explained on the basis of the BCS theory. Previous approaches to this problem were based on the average conductivity model, the London and the two-fluid models. It is shown that they are not able to explain the observed χPrime;-peak at T_c and are basically, not adequate for the treatment of such a problem.     

Linear and nonlinear response of discrete dynamical systems

We carry out a linear response theory for discrete dynanmical systems with periodic attractors. The symmetry properties of the susceptibility matrix are studied and its eigenvalues and eigenvectors are determined. Close to a period-doubling bifurcation where the susceptibility diverges, its half-width is related to the Lyapunov exponent. At the transition to chaos the susceptibility has some universal behaviour which is described by a critical exponent κ=1?(ln2/lnδ)=0.550193... At the bifurcation points where linear response theory becomes insufficient we also determine the nonlinear response.     

Scaling of vortex transport properties and nonlinear ac response of high-temperature superconductors

The macroscopic behavior of high-temperature superconductors is described by a nonlinear response function in combinations with Maxwell equations. This function is compatible with the suggested different model pinning barriers U(J). A comparison of this function to the scaling behavior of the isothermal current-voltage characteristics measured in twinned YBa₂Cu₃O (YBCO) samples shows fair agreement. We also compare the amplitude dependence of ac susceptibility derived from this function with several experimental results of high-temperature superconductors and find a general power law in the out-of-phase peak shift. Received 4 August 1999 and Received in final form 30 November 1999     

Linear and nonlinear response of the avalanche breakdown far-infrared photodetector

It is found that the Avalanche Breakdown far-infrared photodetector responds linearly with incident power, i_s ∝ P_s, when subjected to a specially coherent signal, for example to the beam of a free electron laser, but responds according to a law, i_s ∝ P^β_s, with 0.5 ⩽ β ⩽ 1.0, when irradiated with incoherent radiation, as from a multimode far-infrared laser. Here the detector signal current is i_s and the incident signal intensity is P_s.     

Kq, Scaling of ac susceptibility and the nonlinear response function of high-temperature superconductors

The amplitude-dependent ac susceptibility of high-temperature superconductors is shown to obey some empirical scaling relations. We try to analyze this behavior by extending a dc nonlinear response function of mixed state to the ac cases. The derived equations for critical current and ac susceptibility ξ(T) agree with the scaling relations of experimental data.     

Structural phase transition in the mixed state of superconducting films in a parallel magnetic field

A thin film of a second-kind superconductor in a magnetic field parallel to the surface of the film is considered in the London approximation. It has been shown that if bulk pinning is absent and the suppression of super-conductivity by the magnetic field is negligible, the splitting of a vortex chain in the film occurs as a structural phase transition either of the first or second order, depending on the ratio of the thickness of the film d to the penetration depth of the magnetic field λ. The ratio d/λ, and thereby the character of the transition in the vortex lattice, can be changed by varying the temperature. The corresponding critical thicknesses of films and field ranges in which this effect can be observed experimentally have been calculated.