Vortices in anisotropic type-II superconductors

We present a generalized variational model of an isolated vortex, valid in the anisotropic case when the external magnetic field is along one of the symmetry directions. We discuss the effects of the field anisotropy on the core and magnetic pinning of individual vortices.     

Elementary pinning potential in type II superconductors nearH c2

The elementary pinning potential of a small defect in a type II superconductor is calculated near the upper critical magnetic field. The calculation applies at all temperatures and all background impurity contents of the metal. The pinning potential is found to decay according to the inverse impurity parameter when other impurities are added. A very simple formula for the pinning potential is obtained in the Ginzburg-Landau region. The boundary condition to be imposed on a Ginzburg-Landau theory at small defects is derived.     

Local structure and thermodynamic properties of clean type II superconductors nearH c1 at arbitrary temperature

An iterative procedure has been developed to solve Eilenberger's version of the Gor'kov equations numerically. The method has been used to compute the structure of flux lines and the lower critical field for clean superconductors as a function of temperature. Some information on the vortex lattice has also been obtained by means of a circular cell approximation. We find a pronounced reduction in the size of the coreregion (measured, e.g., in units of the temperature-dependent coherence length) with decreasing temperature; this results in considerably steeper slopes of the order parameter and the current density at the vortex center. There are indications that, among other peculiar effects, these slopes diverge forT → 0. The field at the center of the isolated vortex apparently increases with decreasing temperature down toT=0. The results are compared with experiments and with similar calculations for the dirty limit.     

Linear response and instability of vortex lattice in type-II superconductors

The wave vector dependent linear response of the vortex lattice in type-II superconductors is studied by calculating the superfluid density and is shown to have a singular behavior with respect to the long wave length perturbation of vector potential. The calculations are carried out in terms of the nonlinear elastic theory of the vortex lattice, which is, in principle, a low temperature expansion, and the terms up to the first order in temperature are taken into account, which is beyond the usual Gaussian elastic theory. The superfluid density is found to behave as ~ k_BT ¦k¦² log ¦k¦,for the small wave vector,k,perpendicular to the external magnetic field, where Tand k_B are the temperature and the Boltzmann constant, respectively. This behavior causes the divergence of the magnetic susceptibility at a critical wave vector, k_c.We show that this behavior is associated with an instability of vortex lattice to the externally applied perturbation.     

Hall effect in the vortex state of dirty type-II superconductors

The off-diagonal component of the conductivity tensor of dirty type-II superconductors is calculated in the magnetic field nearH _c2 . Contributions come from both the fluctuation and static parts. The former is the Ginzburg-Landau (GL) term, whose origin is the motion of Cooper pairs, and is obtained to the order ofT/ _F as the result of the energy dependence of the density of states near the Fermi surface. The latter is obtained to the order of _c . By use of the diagonal component of the conductivity tensor given by Thompson, Takayama, and Ebisawa, the derivative of the Hall angle with respect toH is calculated; it agrees qualitatively with the observed behavior.A part of Ph.D. thesis submitted to University of Tokyo, 1971.Work supported by the Research Institute for Fundamental Physics, Kyoto University.     

Attractive interaction between vortices in type-II superconductors at arbitrary temperatures

We show that attractive interaction between vortices occurs when Re(^–1)> ₀ ^–1 for type-II superconductors with local or nonlocal magnetic effects, where [Re(1/)]^–1 and ₀ are, respectively, the decay length of the magnetic field and the order parameter at arbitrary temperatures. The interaction between vortices is attractive for all those type-II superconductors in which field reversal occurs, but field reversal is not a cause of attractive interaction. On the other hand, oscillatory behavior of magnetic fields contributes to attractive interaction. The critical values of the Ginzburg-Landau parameter, below which attractive interaction occurs, satisfy essentially the equation Re (^–1)= ₀ ^–1 .Work supported by the National Research Council of Canada and Alexander von Humboldt Foundation.     

Viscous flux motion in anisotropic magnetic superconductors

Magnetic field penetrates in the form of flux lines or vortex thread into type-II magnetic superconductors (MSC) and induces magnetization of magnetic subsystem over a distance of an order of the London penetration depth surrounding the normal cores. When a flux line moves by, surrounding magnetization moves as a whole through the sample and a free motion of vortices is subjected to magnetic viscous drag, giving rise to dissipation. The flux flow resistance in the mixed state of anisotropic MSC has been studied on the basis of the London theory. Expressions for the dissipation and viscosity coefficient associated with the change of the magnetic subsystem as a vortex moves about are derived.     

Inelastic neutron scattering from the vortex lattice in type-II superconductors. I

The inelastic neutron scattering from the vortex lattice in dirty type-II superconductors is considered. In the high-field region, the correlation function for the local magnetization is given in terms of the fluctuation propagator of the superconducting order parameter. In particular it is shown that the Fourier transform of the correlation function for the local magnetization diverges as /q –G _i /^–2, when the transverse transfered momentumq approaches the reciprocal lattice vectorG _i of the Abrikosov lattice. This term gives rise to tails around each Bragg peak in the inelastic neutron-scattering cross section.     

Specific heat of type-II superconductors in magnetic fields nearT c

The GLAG theory predicts that the value of the specific heatC _M in the mixed state just below the transition to the normal state, is a function of the Ginzburg—Landau (GL) parameter , even for vanishingly small magnetic fields(TT _c ).C _M is thus different from the specific heatC _S in the pure superconducting state(H=0) for all except 1.9. Experimental results of the authors generally confirm this paradoxical prediction which is not in contradiction with the thermodynamics of phase transitions. To experimentally clarify this behavior close toT _c , Nb₈₀Mo₂₀(4) and Pb₉₈In₂(0.8) specimens are studied in fields much smaller than those usually applied (down to17 Oe). A new method for measuring specific heat in decreasing as well as increasing temperature is introduced. Very good agreement with the theory is found for fields higher than 120 Oe while a deviation is observed close toT _c for lower fields where values of the Abrikosov lattice parameter would become larger than 1 µ. The sense and the magnitude of the deviation are such thatC _M andC _S would be equal for fields of 20 Oe and below. Possible explanations are discussed. It is suggested that a fundamental modification of the vortex state structure occurs in small fields close toT _c .     

Irreversible thermodynamics for vortex motion in type II superconductors

Irreversible thermodynamics consideration is applied to give a systematic discussion of dissipative processes involving vortex motion in superconductors.     

Vortex motion in high-T c superconductors near the upper critical fieldH c2

The vortex dynamics in layered superconductors such as YBaCuO and BiSrCaCuO near the upper critical field H_c2 is considered. The magnetic field is parallel to the layers and a transport current flows along the layers perpendicular toH. There exists a finite pinning force for the vortex motion across the layers in a macroscopically homogeneous superconductor. The critical current vanishes exponentially in the limit of weakly layered structure, _c (T)s. The current-voltage characteristic is calculated in case _c (T)s. The initial part of the characteristic may have a negative slope depending on the magnetic fieldH.     

Paraconductivity in type-II superconductors

The additional conductivity due to the fluctuation of the order parameter in dirty type-II superconductors is reconsidered. It is shown that in a magnetic fieldH slightly above the upper critical field the electric conductivity is strongly anisotropic depending on the relative direction of the magnetic field and the electric current. In the parallel case (i.e.,H J) the conductivity diverges like(H–H _c2)^–3/2, while in the perpendicular case (H J) it diverges like(H–H _c2)^–1/2.     

Inelastic neutron scattering from vortex lattice in type-II superconductors. II. The London model

The inelastic neutron scattering from the vortex lattice in type-II superconductors is considered. Use is made of the London model to describe the vibration of the vortex lattice. We find that the differential cross section has sharp peaks besides the Bragg peaks when the transferred momentumq approaches the reciprocal lattice vectorG. These peaks are due to excitation of the vibrational modes and diverge as ¦q –G¦^–2. We also calculate the Debye-Waller factor, which is extremely small.     

Statics and dynamics of the vortex lattice in high-T c superconductors

Some properties of the flux-line lattice in conventional and high-T_c supperconductors are reviewed, with particular stress on phenomenological theories, magnetization curves, vortex lattice in films, nonlocal elasticity, phase diagram of vortex arrangements, vortex dynamics, and geometry effects.     

Hall effect of a dirty type II superconductor nearH c2

The theory of the Hall effect of dirty, type II superconductors nearH _c2 by Ebisawa based on the free-electron model is extended to the case of isotropic but arbitrary energy—momentum relation. It is also shown that the detailed form of the impurity potential, i.e., the momentum dependence of its Fourier transform, which is neglected in Ebisawa's work, also contributes to the effect and its contribution is calculated. The result shows that, besides the energy dependence of the density of states and electron velocity near the Fermi energy of the host metal, the detailed nature of the impurity also has a large influence on the Hall effect. The theory is compared with experiment.On leave of absence from Research Institute of Electrical Communication, Tohoku University, Sendai, Japan.     

Pinning in superconductors with anisotropic defects

By calculating the volume pinning force in superconductors with anisotropic pinning centers we have shown that the critical current densitiesj _c in NbTi by both current and magnetization measurements can be explained. The critical current density in fields parallel toj _c can also be included. We conclude therefore that in superconductors with strong pinning centers the critical state is always determined by the equilibrium condition between the Lorentz force and the volume pinning force and not by the instability of the force-free configuration. By detailed investigation of thej _c dependence on field direction, useful information can be obtained with respect to the volume and surface contributions to the pinning force.     

ac magnetic instability in non-ideal type-II superconductors

The theoretical approach is carried out with the combined thermal and magnetic equations which are based on the critical state model for non-ideal type-II superconductors and include controllable physical parameters. Also, the behaviour of flux jumps is studied on Nb-Ti-Zr ternary alloy wires in the temperature region 1.8–9.0 K under various heat transfer conditions. The ac field method applied here has the advantage of determining flux jump fields more exactly than the linear sweep method.     

Time relaxation of magnetization in type-II superconductors

We assume that currents induced by isothermal changes of magnetic field decay logarithmically with time. Incorporating this time dependence into the critical state model, we obtain logarithmic relaxation rate of magnetization as a function of field for the case of an infinite cylinder. We compare these calculations with our earlier calculations on infinite slab geometry.     

Dynamic motion analysis of optically trapped nonspherical particles with off-axis position and arbitrary orientation

We present a general computational method of determining radiation pressure forces and torques exerted on small particles by a converging beam of light. This method, based on a ray optics model of optical trapping, allows time-series dynamic motion analysis to be performed on nonspherical objects that are initially positioned off the optical axis with arbitrary orientation. Comparison tests of computer simulation with experimental results prove that the proposed model can be used to predict complicated trapping behavior of microfabricated objects.