Stability of normal state bubbles in the intermediate state of type I superconductors

The intermediate state in a type I superconducting Indium slab is observed with the high resolution magneto-optical imaging technique. The patterns consist of coexisting cylindrical-shape (bubbles) and elongated-shape (lamellae) normal state domains surrounded by the superconducting phase. We show that the shape cylindrical or elongated of the domains is correlated to their surface area. Those first experimental results indicate that there is a maximum surface area above which bubbles are no more observed. This maximum surface area is found to coincide with the stability limit of the bubble shape.     

The thermoelectric power of type I superconductors in the intermediate state

Measurements of the thermoelectric power of superconducting indium in the intermediate state are reported. A large maximum in the thermoelectric power of crystalline indium is observed with the intermediate state value exceeding the normal state value in the temperature range 0.3 < T/T_c < 1. No maximum is observed in polycrystalline indium.     

Passive measurement of flux nucleation in the current-induced resistive state of type I superconductors

Flux-tube nucleation rates have been measured in the current-induced resistive state of type I superconducting In films between 1.5 and 2.0 K by a completely passive technique. Indication of periodic nucleation is observed only in narrow regions of sample voltage drop, whose position is a sensitive function of temperature. Frequency bandwidth measurements of the nucleation rate yield a spectral purity of one part in 10⁴ within the narrow regions where an experimental signal can be detected.Supported by a grant from the Deutsche ForschungsgemeinschaftAlexander von Humboldt Foundation Fellow     

Excitation spectrum of type I superconductors in high magnetic fields

The paper is devoted to the theoretical investigation of the energy spectrum of surface excitations in type I superconductors placed in a magnetic field. The case of strong fields has been considered when the renormalization of the gap near the superconductor's surface becomes essential. Then there arise excitations that are localized in a superficial layer comparable in thickness with the length of coherence ξ. For this case the energy density of states of the surface excitations has been also analyzed.     

Dynamics of local magnetic flux vortexes in superconductors

The dynamics of local magnetic flux vortexes in high-temperature semiconductors is studied with a mechanical method. Physical conditions in a gradient magnetic field are analyzed. Obtained results are treated within a model of free and pinned vortexes. The magnitudes of elastic modula, pinning strength, dissipated energy, viscous friction of the vortexes, and pinning potential were calculated. The method allows the determination of local, rather than integrated, superconductor characteristics. This makes it possible to map pinning centers over the crystal structure.     

Current induced intermediate state in thin film superconductors

High-resolution magneto-optical studies of the current-induced intermediate state in superconducting lead films indicate a magnetic structure consisting of chains of flux tubes rapidly moving along channels from both edges to the center of the strip. At increasing levels of the transport current new flux tube channels are created abruptly, resulting in relatively large resistive voltage steps.     

Vortex avalanches and magnetic flux fragmentation in superconductors

We report the results of numerical simulations of nonisothermal dendritic flux penetration in type-II superconductors. We propose a generic mechanism of dynamic branching of a propagating hot spot of a flux flow/normal state triggered by a local heat pulse. The branching occurs when the flux hot spot reflects from inhomogeneities or the boundary on which magnetization currents either vanish, or change direction. The hot spot then undergoes a cascade of successive splittings, giving rise to a dissipative dendritic-type flux structure. This dynamic state eventually cools down, turning into a frozen multifilamentary pattern of magnetization currents.     

Resistive states of the composite superconductors at magnetic flux creep

The effect of magnetic flux creep on the formation of resistive states of the composite superconductors has been studied taking into account their self-heating. The obtained results have been compared with the calculations carried out using the existing thermal stabilization theory, which is based on the model of a stepwise transition from the superconducting to normal state. It has been shown that, over a wide range of the superconductor temperature, this model leads to overrated effective electric resistances of the composite. As a result of its stable self-heating, the notions on the critical current, which determine the maximum transport current and on the resistive transition temperature, the higher of which in the transport current begins dividing between the superconductor and matrix, a loss a physical sense at magnetic flux creep, are used in the existing thermal stabilization theory. As a result, the limits of the theory of thermal stabilization of the composite superconductors can be extended if the theory has been used to describe stable sates at currents, which are higher than the conditionally defined critical current of the composite.     

Equilibrium topology of the intermediate state in type-I superconductors of different shapes

A high-resolution magneto-optical technique was used to analyze flux patterns in the intermediate state of bulk Pb samples of various shapes - cones, hemispheres, and discs. Combined with the measurements of macroscopic magnetization, these results allowed studying the effect of bulk pinning and geometric barrier on the equilibrium structure of the intermediate state. Zero-bulk pinning discs and slabs show hysteretic behavior due to topological hysteresis - flux tubes on penetration and lamellae on flux exit. (Hemi)spheres and cones do not have a geometric barrier and show no hysteresis with flux tubes dominating the intermediate field region in both regimes. It is concluded that flux tubes represent the equilibrium topology of the intermediate state. Real-time video is available in the EPAPS Document No. E-PRLTAO-98-024726..     

Anomalous attenuation of longitudinal ultrasound in the intermediate state of pure type I superconductor

The dependence of ultrasonic attenuation on the direction of magnetic field H (H ⊥ k) in intermediate state of very pure gallium at T = 0.5°K was found to be anomalously different from the dependence observed at the same temperature and H = H_c in normal state. This phenomenon can be explained taking into account the anisotropy of the gallium Fermi surface.     

Fluctuations and defects in the spiral state of magnetic superconductors

We want to point out three properties of a magnetic superconductor: (i) The absence of true long-range order in the spiral state leads to the structure functions behaving like (q₆ ? q₀)^η?2 and (q²_⊥)^η?2 for q_⊥=0 and q₆=0, respectively, where q₀ is the preferred momentum. The indices η are measured via Bragg-like neutron scattering. (ii) The state is perforated by line-like defects. (iii) Above some critical temperature the defect lines proliferate, thereby destroying the spiral quasi-order.     

Fluctuations in the flux nucleation process of the current-induced resistive state in type-I superconductors

The fluctuations of the flux-tube nucleation frequency ^* in the current-induced resistive state have been studied using a strictly passive micro-fieldprobe as a flux-tube counter. The measurements were performed with constricted indium films near 2.0K. They included both the bandwidth of the rf signal from the field probe and the temporal variations of ^*. From a comparison of the power spectrum of the noise voltage and of the function ^*(t) the relative importance of the fluctuations in the size and in the nucleation frequency of the flux tubes can be evaluated. In addition to fluctuations ofv ^* around an average value, switching between two frequencies ₁ ^* and ₂ ^* can be observed. As a function of sample voltage the bandwidth shows oscillations which appear to be associated with the change in the time-averaged number of flux tubes traveling simultaneously through the constricted film. Narrow-band flux nucleation with ^*/ ^*<10^–1 is observed only in rather restricted regimes of the sample voltage.Supported by a grant from the Deutsche Forschungsgemeinschaft     

Theory of magnetic impurities in superconductors. I

The Nagaoka Green's functions equations for a superconductor are solved exactly and the question of bound states within the gap is answered unambiguously. It is shown that there are always two bound states symmetrically located with respect to the center of the gap. For ferromagnetic coupling,γ>0, and for antiferromagnetic coupling, butT _K ?T _c0 orT _K ?T _c0, these bound states are very close to the gap edges. ForT _K ～T _c 0, however, the bound states move towards the center of the gap. It is pointed out that in the latter case important deviations from the Abrikosov-Gorkov theory, i.e. manifestations of the Kondo effect, should occur which could be tested experimentally by investigating the density of states.     

Critical state theory for nonparallel flux line lattices in type-II superconductors

Field penetration profiles in type-II superconductors with nonparallel vortex configurations are obtained by a proposed least action principle. We introduce a functional C[H-->] which is minimized for the current density constrained by J-->inDelta(H-->,x-->), where Delta is a bounded set. Within the isotropic case /J-->/< or =J(c)(H), the profiles H-->(x-->,t) are derived for an applied changing excitation. The model can reproduce the physical phenomena of flux transport and consumption, and the magnetization collapse in crossed field measurements.