Meissner superconductors

It is perfectly diamagnetic, i.e. it completely excludes applied magnetic fields. This is the Meissner effect and is the reason why a superconductor can levitate a magnet. 

This solution motivates the existence of a complete Meissner effect for all gauge fields inside quark superconductor. It corresponds to the absolute minimum value of free energy Fmin = Fn — 3a2/2A2 in the bulk. 

Twenty years later, in 1933, the German physicist Walter Meissner (together with his co-worker Robert Ochsenfeld) discovered that superconductors cannot be crossed by magnetic field lines. This property is today defined as the Meissner effect. 

The so-called phenomenon of levitation of a magnet placed above a superconductor, Figure 4, is a direct consequence of the Meissner effect. 

Figure 3 The Meissner effect. A superconductor (here in a circular section) excludes the magnetic field lines when it is frozen below the critical temperature...

Figure 2 The Meissner Effect, or the levitation of a strong magnet by the internal diamagnetic field of a high Te superconductor. 

In one sample, the crossover from the metallic (Pauli paramagnetic) region to the diamagnetic state occurred at 32 K. The diamagnetism measured was rather weak, on the order of 1% Meissner fraction, as compared to a pure superconductor (-1/47T, the full Meissner effect). 

Discovery of the 90+ K Superconductor "Paul" Chu and coworkers at the University of Houston (during October 1986) carried out the synthesis of (La1.xBax)CuOs.y (Type I) and (La1.xBax)2 Cu04.y (Type II) compounds and isolated superconducting phases exhibiting a sharp decrease in resistivity at 32 K. The best materials, however, showed only a 2% Meissner fraction. By applying pressure to one such product, their forte in superconductor research, they observed an increase in transition temperature of 8 degrees at 14 kbar pressure (see Figure 29). Chu, et al., submitted (156) these results to Physical Review Letters on 15 December 1986, and the publication appeared in the January 26, 1987 issue. 

The purpose of this chapter is not to address the continuing controversy about the electronic nature of the electron-doped superconductors, but rather to review the crystal chemistry of the T -Nd2Cu04 system and give practical details on how to prepare crystallographically pure electron-doped superconductors in ceramic or single-crystal form with high Meissner fractions. 

The two-phase nature of all ceramic samples of the electron-doped superconductors probably accounts for their less desirable properties, including low Meissner fractions in many samples, low and nonmetallic conductivity in the normal state, and... 

The discovery of thallium containing superconductors (4) was another important development. Several superconducting phases exist and consist of intergrowths of rock salt (TI-O) and perovskite layers. They have been reported with zero resistance and Meissner effect up to 125K, i.e., with the highest critical temperatures discovered so far. 

The Meissner effect is a very important characteristic of superconductors. Among the consequences of its linkage to the free energy are the following (a) The superconducting state is more ordered than the normal state (b) only a small fraction of the electrons in a solid need participate in superconductivity (c) the phase transition must be of second order that is, there is no latent heat of transition in the absence of any applied magnetic field and (d) superconductivity involves excitations across an energy gap. 

For more than 20 years, little progress was made in the understanding of superconductors and only more substances exhibiting the effect were found. More than 20 metallic elements can be made superconducting under suitable conditions (Figure 10.2), as can thousands of alloys. It was not until 1933 that Meissner observed a new effect. 

In addition to the zero resistivity, superconducting materials are perfectly diamagnetic in other words, magnetic fields (up to a limiting strength that decreases as the temperature rises toward Tc) cannot penetrate them (the Meissner effect). This is a consequence of the mobile, paired state of the electrons. Indeed, it is the demonstration of the Meissner effect, rather than lack of electrical resistivity, that is usually demanded as evidence of superconductive behavior. One entertaining consequence of the Meissner effect is that small but powerful magnets will float (levitate) above the surface of a flat, level superconductor.30... 

A superconductor is a material that loses all electrical resistance below a characteristic temperature called the superconducting transition temperature, Tc. An example is YBa2Cu307 (Tc = 90 K). Below Tc, a superconductor can levitate a magnet, a consequence of the Meissner effect. 

The repulsive force of the expulsion of these field lines, known as the Meissner effect, leads to the phenomenon of levitation — a magnet placed above a superconductor floats suspended above the top of the superconductor. 

Superconductivity dates back to 1911, when a Dutch physicist determined that the element mercury, when cooled to minus 452 degrees Fahrenheit, has virtually no electrical resistance. That is, it lost zero electric power when used as a means to distribute electricity from one spot to another. Two decades later, in 1933, a German physicist named Walther Meissner discovered that superconductors have no interior magnetic field. This property enabled superconductivity to be put to commercial use by 1984, when magnetic resonance imaging machines (MRIs) were commercialized for medical imaging. 

If a Type I superconductor such as lead is placed in a small magnetic field (e.g. a few mT) and cooled, then at 7[. the magnetic field is expelled from the interior of the specimen. This is the Meissner effect, which is fundamental to the superconducting state it is not simply characteristic of a material which happens to be a (fictitious) perfect conductor. The total absence of an electric field in a... 

The irreversibility field (Hirr) Figure 4.56 illustrates the events as a magnetic field is applied to and then removed from a Type II superconductor below its critical temperature. At applied fields up to Hcl the response of the material is as expected for a Type I material. That is the field is excluded (the Meissner effect) and the material behaves as a perfect diamagnetic. At applied fields above Hcl there is some flux penetration and this increases until the material becomes normal at Hcl. 

A superconductor exhibits perfect conductivity (See Section 7.2) and the Meissner effect (See Section 7.3) below some critical temperature, Tc. The transition from a normal conductor to a superconductor is a second-order, phase-transition which is also well-described by mean-field theory. Note that the mean-field condensation is not a Bose condensation nor does it require and energy gap. The mean-field theory is combined with London-Ginzburg-Landau theory through the concentration of superconducting carriers as follows ... 

The Meissner effect is the exclusion of an external magnetic field from the bulk of the superconductor. By London theory the magnetic induction is... 

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