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Superconducting Elements If mercury is cooled below 4.1 K, it loses all electric resistance. This discovery of superconductivity by H. Kammerlingh Onnes in 1911 was followed by the observation of other metals and intermetallic compounds (made of two or more metallic elements) which exhibit zero resistivity below a certain critical temperature Tc. The fact that the resistance is zero has been demonstrated by sustaining currents in superconducting lead rings for many years with no measurable reduction. Table 13-03 shows the elements, which can become superconducting at the indicated critical temperature.

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Table 13-03 Super-conducting Elements

Superconducting Compounds Ceramic materials are expected to be insulators -- certainly not superconductors, but that is just what Georg Bednorz and Alex Muller found when they studied the conductivity of a lanthanum-strontium-copper oxide ceramic in 1986. Its critical temperature of 30 K was the highest, which had been measured to date. Their discovery started a surge of activity which discovered superconducting behavior as high as 125 K. However, these compounds are hard to make and difficult to shape. They pose a multitude of physical challenges to researchers and engineers.

Figure 13-07 High Temperature Superconductors [view large image]

Figure 13-07 lists the high temperature (above 4o K) superconductors discovered during the last one hundred years.

Superconductivity Meissner Effect

The effect of superconducting is often demonstrated by cooling a disk made of superconducting material with liquid nitrogen to below the critical temperature Tc. A magnet placed above the disk is repelled, i.e., it is levitated above the superconductor. (See Figure 13-08a.) This phenomenon is caused by the Meissner effect which is related to the fact that a superconductor will exclude magnetic fields within the superconducting material (see Figure 13-08b).

Figure 13-08a Superconductivity

Figure 13-08b Meissner Effect

Suppose, as in Figure 13-08a, a magnet is placed above a superconductor. The induced magnetic field inside the superconductor is exactly equal and opposite in direction to the applied magnetic field, so that they cancel within the superconductor. The result are two magnets equal in strength with poles of the same type facing each other. These poles will repel each other, and the force of repulsion is enough to float the magnet. However, the magnet's magnetic field must be below the superconductor's critical magnetic field Hc. If the magnetic field is stronger than Hc it would penetrate the superconductor and extinguish the superconductivity.

In 1956 L. Cooper offered an explanation for this phenomenon of superconductivity. The process starts in some materials at very low temperature when two electrons near the Fermi energy level could couple to form an effective new particle, under a very weak attractive force.
Cooper Pair This particle was subsequently called the Cooper pair (Figure 13-08c). It can be shown that the most energetically favourable situation for this to occur was when the two electrons had a total spin of zero. Since the Exclusion principle does not apply to particle with integer spin, there is no restriction on the energy state that the Cooper pair can occupy. In particular, at low temperatures thermal agitation is minimal, and all of the Cooper pairs can occupy the lowest possible energy state. Thus no energy exchanges can take place (nothing to give), the normal resistive energy losses are not possible. The Cooper pairs move unimpeded through the superconducting material: it has

Figure 13-08c Cooper Pair [view large image]

zero electrical resistance and exhibits superconductivity. The weak attractive force between the electrons in the Cooper pair has its origin in the induced polarization (of the atoms in the lattice, see Figure 13-08c).
An equivalent description is to consider the attraction as the result of the emission of a virtual phonon by one electron and its absorption by another one as shown by the Feynman diagram in Figure 13-08c.

This is known as the BCS theory. It does not explain the absence of resistance in copper oxide based compounds. There is still no definitive theory of how or why these compounds become superconductivity.

It has been shown that the exclusion of magnetic flux (Meissner effect) corresponds to a finite range for the electromagnetic field and hence to a `massive photon'. In the context of quantum field theory, the meissner effect in a superconductor occurs because the U(1) gauge symmetry is broken in a superconductor. The photon acquires a mass through the Higgs mechanism and the Higgs bosons are the Cooper pairs.

Super-conductivity is often cited as an example of emergent phenomenon when novel property appears in an ensemble of individual parts. The human brain is another example where ensemble of molecules and atoms becomes a conscious whole. Very often the emergent property is the result of internal force (between the parts) winning over thermal motion (ultimately the tendency toward higher entropy - more disorder).
Strange Metal Entenglement It was discovered in 2008 that some materials such as the barium iron arsenide (BaFe2As2) behave strangely at low temperature. It starts out in a state of spin-density wave (SDW) in which the charge density (of the conduction electrons) has a sinusoidal modulation out of step from the periodicity of the crystal lattice. This material become super-conductive with doping (substituting arsenic with phosphorus as illustrated in Figure 13-08d) but only up to about 30% beyond which it turns to the normal state of Fermi liquid (free Fermi gas). Another interesting property is displayed by increasing the temperature at 30% doping level, the result is neither a superconductor nor SDW but something called strange metal. This phenomenon cannot be explained by the BCS theory. It seems that all the

Figure 13-08d Stange Metal [view large image]

Figure 13-08e Entanglement [view large image]

electrons in the solid entangled together as a single indivisible whole. It turns out that such complicated system has a counter part in Superstring
theory, from which a simpler formulation can be found by the method of duality. According to the Superstring theory, the entanglement acts as an addition spatial dimension above and beyond the three dimensions where the electrons reside (Figure 13-08e). However, scientists still don't understand how such state occurs in actual materials. Explaining what is really going on is still in its infancy. It should be emphasized that this is just a mathematical analogy; the wholesale entanglement does not constitute a proof for the existence of extra-dimensional space.

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