Experimental Evidence for Delayed Entry of Flux Into a Type-II Superconductor

Abstract

The temperature dependence of EQ/E-comes from the factor C V T. The line in Fig. 1 represents the fit of (EQ/EJ) to the product of T and a Debye specific-heat function. This is a twoparameter fit; the Debye temperature is found from the fit to be 14.8°K and the low-temperature limit of (EQ/E^ to be Eo/E f = 1. 6 x 1CT 7 T 4 . At very low temperatures all of the thermally excited phonons interact with the electrons and C v is the total lattice specific heat of the crystal. Thus, the right-hand side of Eq. (3) involves no adjustable parameters in the low-temperature limit. Using values measured on our specimen for JLI, W, and t, and Bryant and Keesom's 5 value for C v , in Eq. (3) gives EQ/EJ = 1.1 xKT 7 T 4 , about two thirds of the measured value. value.The value of 0, the effective Debye temperature of the interacting phonons, is a measure of q m , the maximum wave vector of the interacting phonons, or of the number of phonon modes which interact with the electrons. The observed value, 9 = 14. 8 °K, corresponds to 8 x 10 18 modes per cm 3 , in other words, about one mode per electron. Although calculation of the number of phonons which drift with the electrons is difficult because of the anisotropy of the electronic energy bands, we would have expected that the electronic motion would impart the drift velocity to a large Null-deflection torque magnetometer studies 1 ' 2 have been carried out on annealed homogeneous Pb-Tl alloys (4. 3-12. 3 at.% Tl) in the form of thick films (1.4-4.2 /i) and foils (25-100 jx) over the interval 1.1 ^ T < 4.2°K, with the applied field H very nearly in the plane of the specimen. By this method, the measured field dependence of the torque r defines a characteristic field H T at which T/H departs from its initially linear dependence on H. The departure from linearity can be ascribed to flux penetration, in accord with our measurements on thick annealed pure Pb films which exhibit linear T/H behavior until number of phonons. In the case of a spherical Fermi surface, phonons with wave vector less than twice the Fermi wave vector can scatter electrons directly. The sphere of such directly interacting phonons in wave-number space contains 12 phonon states (including the three polarization branches) per electron. Since each of the electron valleys contain 1/4 of the electrons, the number of directly interacting phonons might be reduced to three per electron. However, because not all valleys interact with the same phonons, the number should be somewhat larger than three. The number might be reduced if the higher energy scattered phonons had short momentumloss relaxation times, so that they remained in equilibrium even though scattered by the electrons.

Stability Limits of the Meissner State and the Mechanism of Spontaneous Vortex Nucleation in Superconductors

“…We have also plotted % x as determined from Eq. (9) and the amplitudes of the current variations j as determined from Maxwell's equation curl curl q=-j. This leads to jx = (1 -Q 2 ) $x sinky; j y = (1 -3Q 2 ) q y cosky,…”

First vortex entry into a perpendicularly magnetized superconducting thin film

“…11 Indirect experimental verification of the superheating field and the correlation with the above-described models was based on detecting the onset of the nonlinearity of the initial magnetization in bulk superconductors. [12][13][14] We propose here a more direct and reliable way to determine the superheating field by imaging, with single-vortex resolution, the first entered vortex in a thin superconductor. In order to achieve this goal, a careful sample design and fabrication are necessary.…”

Flux Penetration in an Anisotropic Type-II Superconductor

“…Equation (4) is analogous to the Schrodinger equation for a harmonic oscillator whose lowest eigenvalue is given by \a\ =eh(ix 11 Here k 2 is an arbitrary parameter. Tilley goes on to show that the surface nucleation field H c % is related to H c2 just as it is in the isotropic case (i.e., H cZ = 1.69H c2 ), and therefore depends on the direction of the magnetic field in the same way as H c2 .…”