Superconductivity Meissner effect

The authors of Ref. [12] reconsidered the problem of magnetic field in quark matter taking into account the rotated electromagnetism . They came to the conclusion that magnetic field can exist in superconducting quark matter in any case, although it does not form a quantized vortex lattice, because it obeys sourceless Maxwell equations and there is no Meissner effect. In our opinion this latter result is incorrect, since the equations for gauge fields were not taken into account and the boundary conditions were not posed correctly. 

The Meissner Effect and Levitation. Besides the absence of electrical resistance, a superconducting material is characterized by perfect diamagnetism. The exclusion of magnetic field lines from a material when it passes from a normal state to a superconducting state is shown schematically in Figure 3. 

Paul" Chu, and others at University of Houston, also reproduced Zurich s I.B.M. research results (156). Bell Lab s confirmation of Bednorz and Muller s discovery of high Tc superconductivity in copper oxide compounds was published (157) in the Jan. 1987 issue of Physical Review Letters. The electrical resistivity data from their work showing an onset of superconductivity at 36.5 K for the composition Lax gSr0 2Cu04 is plotted as Figure 28. This product also showed a 60-70% Meissner effect. 

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. 

Figure 4 Flux exclusion (shielding) versus increasing temperature (solid triangles) and flux expulsion (Meissner effect) versus decreasing temperature (open triangles) in a 25 Oe external field for a superconducting YE Cu Oy.g single crystal. Exclusion and expulsion are equal for temperatures above the irreversibility point Tjrr (w90.5 K at 25 Oe) Tc is 92 K.

Figure 6.64 Schematic illustration of Meissner effect in which magnetic flux lines that (a) normally penetrate the material are (b) expelled in the superconducting state.

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. 

Similarly, Eq. (911) becomes the equation of the Meissner effect in superconductivity ... 

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 Meissner effect in superconductivity will be argued to be an example of such exclusion. 

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... 

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 ... 

Fig. 12.26. A plot of the maximum superconducting critical temperature with time showing, in addition, the important discoveries of the Meissner effect, the microscopic Bardeen, Cooper and Schrieffer (BCS) theory and the temperature barrier, set by the boiling point of liquid nitrogen. (Reproduced by courtesy of Dr. J.M. Bell,...

The report of the Meissner effect stimulated the London brothers to develop the London equations, which explained this effect, and which also predicted how far a static external magnetic field can penetrate into a superconductor. The next theoretical advance came in 1950 with the theory of Ginzburg and Landau, which described superconductivity in terms of an order parameter and provided a derivation for the London equations. Both of these theories are macroscopic or phenomenological in nature. In the same year, 1950, the... 

There are two aspects to perfect diamagnetism in superconductors. The first is magnetic field exclnsion if a material in the normal state is zero field cooled (ZFC), that is, cooled below Tc to the superconducting state withont any magnetic field present, and then it is placed in an external magnetic field, the field will be excluded from the superconductor. The second aspect is magnetic field expulsion. If the same material in its normal state is placed in a magnetic field, the field will penetrate and have almost the same value inside and outside because the permeability fx is so close to the free space value fXo. If this material is then field cooled (FC), that is, cooled below E in the presence of this applied field, the field will be expelled from the material this is the Meissner effect that was mentioned earlier. 

Figure 2.19. Photograph of the Meissner effect for a rare-earth magnet above a sample of YBCO immersed in liquid nitrogen (from http //www.physics.brown.edu/physics/demopages/Demo/em/ demo/5G5050.htm). The onset of strong diamagnetism ( superdiamagnetism, as observed by the repulsion of an external magnetic field) is the most reliable method to determine superconductive behavior.

In addition to catalytic applications, the perovskite backbone is a key component in modern high-temperature superconductive materials. By definition, a superconductor exhibits no resistance to electrical conductivity, and will oppose an external magnetic field, a phenomenon referred to as the Meissner effect (Figure 2.19). Many pure transition metals e.g., Ti, Zr, Hf, Mo, W, Ru, Os, Ir, Zn, Cd, Hg) and main group metals e.g., Al, Ga, In, Sn, Pb) exhibit superconductivity, many only when exposed to high-pressure conditions. These materials are referred to as Type I or soft superconductors. 

A superconductor is a material which conducts electricity without resistance and the exclusion of the interior magnetic field (Meissner effect) below a certain critical temperature Tc- Superconductivity occurs in a wide variety of materials, including elements, various metallic alloys and some heavily-doped semiconductors. Mixed metal oxides belong to the class of high-temperature superconductors (Tq > 30 K). 

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