Semi-infinite Superconductor Research Articles

Superconductors in parallel field: Electromagnetic properties at the surface

In the framework of the boson transformation method, a general approach to the study of finite-dimensionality superconductors is applied to the investigation of the electromagnetic properties of a semiinfinite superconductor and of a film of arbitrary thickness in the presence of a parallel external magnetic field. The magnetic-field and current density distributions near the surfaces are computed and numerical results are given for some typical cases. As an application, an estimation of the superheating field for type-II superconductor is obtained and compared with previous results.

Surface effects in type-II superconductors

The electromagnetic structure of a quantized flux line is investigated, in the framework of the boson transformation method, for the cases of a semi-infinite superconductor and of a superconducting film of arbitrary thickness. The vortex-antivortex interaction energy is also computed. Comparison with previous results is given.

Surface effects in ferromagnetic superconductors

The behavior of the magnetization near the surface of a semi-infinite ferromagnetic superconductor is investigated theoretically. In contrast to a previous treatment by Kotani et al. [Phys. Rev. B 23, 5960 (1981)] the surface is not described by means of a topological singularity of the phase of the superconducting order parameter. The physical meaning of such a surface singularity is clarified. A mean-field boundary condition $\frac{\ensuremath{\partial}m(0)}{\ensuremath{\partial}x}=\ensuremath{\mu}m(0)$ for the magnetization $m(x)$ is used which allows for a possible strengthening ($\ensuremath{\mu}<0$) or weakening ($\ensuremath{\mu}>0$) of the exchange coupling constant at the surface. The consequences of a nonzero $\ensuremath{\mu}$ for the field penetration and the magnetic surface ordering are pointed out.

Surface effects induced by boson transformation

The boson transformation method is extended to the study of surface effects in macroscopic ordered states. As an illustration, we consider a semi-infinite superconductor and compute the distribution of current and magnetic field around the surface. A qualitative description of the superheating field is also considered.

On the method of Eilenberger for inhomogeneous superconductors

The theory of Eilenberger, modified to take into account the effect of the surface, is applied to the problem of the penetration of a weak magnetic field into a semiinfinite superconductor, and the standard result for the vector potential is derived by linearizing the Eilenberger equations. The dominant term in the asymptotic behaviour is argued to be monotonic for both large and small values of the Ginzburg-Landau parameterk gl . ForT≠ 0, there is a small intermediate range of values ofk gl for which the dominant term is oscillatory, but these oscillations are not related to those found by Eilenberger and Buttner in the isolated vortex problem for smallK gl . From an analysis of these results, we conclude that the absence of the Eilenberger-Buttner oscillations in the field penetration problem cannot be used as an argument against their existence in other problems; in particular, a separate investigation is required for the isolated vortex problem.

Surface nucleation critical fieldH c3(T) of type II superconductors

Near the critical temperatureTc, the thermodynamic potential of a semi-infinite superconductor in an external magnetic field parallel to the surface can be expanded asymptotically in a power series in (1—T/Tc)1/2. In this limit the order parameter decomposes into two parts, the gauge invariant gradient of one of which is proportional to (1—T/Tc)1/2. This part satisfies asymptotically the Ginzburg Landau (GL), the generalized GL-equations and so on. The other part is of non-local nature, is asymptotically non-vanishing near the surface only and influences the boundary conditions for the former part. In general these boundary conditions can be determined to any finite order of (1—T/Tc)1/2 by solving a finite set of inhomogeneous integral equations-all with the same kernel. It turns out thatHc3(T) can be computed up to the order of (1—T/Tc)5/2 for specular and (1—T/Tc)2 for non-specular reflexion without solving the integral equations explicitly. The temperature dependence ofHc3(T)/Tc(dHc2/dT)T=Tc is given up to the orders mentioned above.

Theory of Flux-Flow Noise Voltage in Superconductors

A theory of the time-dependent measured voltage and its associated power spectrum is developed for conditions of magnetic flux flow in the mixed and intermediate states of superconductors. Expressions for the measured voltage, appropriate for flux flow, are given and discussed. The case of a semi-infinite super-conductor containing a single moving fluxoid is then examined as an illustrative model, and potentials and fields are calculated from a London-model description. The resulting time-dependent voltage pulses are computed and shown to depend upon the spatial configuration of the measuring circuit leads. The measured time-dependent flux-flow voltage and the power spectrum arising from an array of fluxoids are formulated and found to depend upon the measuring-circuit configuration, the internal flux distribution, the effects of pinning, and the modes of flux motion. Previous experimental results by van Gurp are interpreted as lending support under certain conditions to a description in terms of flux-line dislocation dipoles proposed by Kramer. New experiments are suggested as tests of the theory.

Critical-Field RatioHc3Hc2for Pure Superconductors outside the Ginzburg-Landau Region. II.T≃Tc

In Paper I we found the appropriate generalization of Gor'kov's linearized gap equation for a pure, semiinfinite weak-coupling superconductor in a magnetic field, separated from vacuum or an insulator by a specularly reflecting surface. In that paper we used the gap equation to study the surface-nucleation critical field ${H}_{c3}$ at $T\ensuremath{\simeq}0\ifmmode^\circ\else\textdegree\fi{}$K. Here we study the region $T\ensuremath{\simeq}{T}_{c}$ and find the first three nontrivial terms in an expansion of the ratio $\frac{{H}_{c3}(T)}{{H}_{c2}(T)}$ to be $1.695[1+0.614(1\ensuremath{-}t)\ensuremath{-}0.577{(1\ensuremath{-}t)}^{\frac{3}{2}}]$, where $t\ensuremath{\equiv}\frac{T}{{T}_{c}}$. The term linear in $1\ensuremath{-}t$ has been found previously, but the last term is new. For $T$ close enough to ${T}_{c}$ we show that the system is accurately described by the linearized Ginzburg-Landau equation with the usual boundary condition and thus regain the results of Saint-James and de Gennes. At lower temperatures the pair wave function has a slowly varying component which satisfies a finite-order differential equation and a surface component which does not. An analysis of the surface component gives an effective boundary condition on the slowly varying part; from this condition the field ${H}_{c3}$ is derived. In combination with the results of Paper I we propose an interpolation formula for the entire temperature range below ${T}_{c}$. A comparison with the available experimental data is encouraging.

An extension of the London equations of superconductivity

A direct extension of the gauge invariant form of the London equations is obtained by means of a reasonably consistent application of macroscopic conservation laws to a two-fluid model. The interaction of the lattice is found to be required and is included in what seems to be a physically sensible but not fully consistent way. The resulting equations permit a spatial variation in the number density of both super and normal electrons because independent partial pressures in each fluid are included. It is assumed that the superfluid carries no entropy, but heat conduction and electrical conduction in the normal fluid are considered along with the associated thermodynamics. The boundary conditions are determined, and one is found to be missing, which difficulty is overcome by utilizing the fact that pure superconductivity disappears beyond some critical value of magnetic field. In a semi-infinite superconductor subject to a static tangential magnetic field the solution indicates an increase in penetration depth with increasing field. In a thin film the solution indicates an increase in the critical field with decreasing thickness. The solutions indicate the possibility of increasing the field beyond the critical value and thereby having partially normal and partially superconducting regions. The surface impedance for a tangetial ac driving field making an angle with respect to the dc field is found to vary with the angle as well as the static field.

Surface Barrier in Type-II Superconductors

The interaction between a flux thread (quantized, fluxenclosing, supercurrent vortex) and the specimen surfuce of a semi-infinite type-II superconductor with a flux thread within it lying parallel to the single plane surface is considered to determine any low-field hysteresis in the magnetization curves of well-annealed, single-phase specimens. (R.E.U.)