Superconductivity is a quantum phenomenon with macroscopic manifestations.

Magnetic levitation with superconductors

A Dutch scientist, Kamerlingh Onnes (this is his last name, by the way), discovered superconductivity about 100 years ago. He noticed that the electrical resistance of mercury drops to zero if the temperature of the sample is reduced below 4K. Simply speaking, the superconductivity is when the Ohmic resistance drops exactly to zero. Superconductivity theory was developed by Bardeen (who is the only man to receive two Nobel prizes in physics), Cooper and Schrieffer. After these people, the theory is abbreviated as BCS.

Superconductivity is one of the most fascinating phenomenon know to mankind. It is an example of a motion with zero friction, i.e. the phenomenon of superconductivity is an example of a perpetual motion machine. If one sets up a current in a loop or a coil made of a superconducting metal, e.g., tin or niobium, and keeps the temperature low enough, the current will run forever, without any battery or any source of electricity attached. The current would not stop even after a 100 years!

The most famous example of mechanical motion without friction is the Earth itself. The Earth orbits the Sun perpetually, without slowing down (perhaps it does slow down, but the rate is negligible-see how the year has always the same duration). The most amazing fact is that no engine is required to continuously push the Earth along its orbit, i.e., around the Sun. In a similar fashion, in superconducting materials electrons participate in a collective flow without friction. They form a huge quantum molecule, called BCS condensate. Due to laws of quantum physics, if a magnetic field is applied to a loop made of a superconducting wire, the BCS condensate begins to circle the loop. This motion never stops because the state with the current is the state with the lowest possible energy of the system.

How important are superconductors? Any U. S. patent application which mentions the term “superconductivity” is immediately submitted to the Department of Defense. This fact shows how important the phenomenon of superconductivity is. Superconducting coils charged with a supercurrent can support magnetic levitation trains, which levitate due to the Meissner effect. Basically, superconductors are diamagnetic, so they repel magnetic field, and therefore any substrate that is magnetized like a permanent magnet.

Superconductors could even provide an explanation to some mysterious prehistoric events. The question of how the Egyptian pyramids and the Stonehenge were built remains a mystery. There are different theories of course. The fact is, scientist really do not know how they were constructed. Some popular theory claims that it took 4,000 men and about 20 years to build the Great Pyramid, with the help of ropes, ramps, pulleys, the natural creativity of the Egyptians, and the political will of the Pharaoh. This is possible, but other possibilities do exist. An Arab historian, Ali al-Masudi, has reported about how heavy stone blocks were transported. He said, a "magic papyrus" (paper) was placed under the stone to be moved. Then the stone was struck with a metal rod that caused the stone to levitate and move along a path paved with stones and fenced on either side by metal poles. The stone would travel along the path, wrote al-Masudi, for a distance of about 50 meters and then settle to the ground. The process would then be repeated until the builders had the stone where they wanted it. This resembles somewhat the operation of the Maglev train. Is it possible that our ancestors employed room temperature superconductivity and levitation? One objection to this is that the Earth field is too weak. Yes, but if Druids and their cousins Egyptians knew the phenomenon of superconductivity, they could have discovered how to make strong permanent magnets as well.

At present time we know that superconductivity occurs in certain materials if they are cooled below some critical temperature. For example, lead becomes superconducting at a temperature of 7.196 K and the BiSrCaCuO compound looses its resistance at about 120 K. The superconductor has zero resistance below the critical temperature, which is called the critical temperature, Tc. The Meissner effect, which is the repulsion and complete expulsion of the magnetic field from the interior of the superconductor, begins to show up at the same critical temperature.

The theory of superconductors was developed by John Bardeen, Leon N. Cooper, and J. Robert Schrieffer. John Bardeen was a true genius, he was one of the inventors of the transistor and won not one but two Nobel prizes in physics. Nobody else won two Nobel prizes. The theory is called BCS theory. It describes how the electrons in the superconducting metal glue together and form a fascinating quantum object called BCS condensate. An interesting property of the BCE condensate is that , according to Heisenberg uncertainty principle, it is not possible to say exactly how many electrons are involved in the condensate, yet one can be absolutely certain that this number is an even number. This is the well know parity effect of superconductivity, which leads to the idea that electrons “marry” and form electron-electron pairs. In reality there are no pairs, but there is a condensate of an even number of electrons.

Superconductors are used to make extremely sensitive devices which can measure magnetic fields of a brain. They are called SQUIDs, which means superconducting quantum interference devices. Superconductor mind reading helmets are tested in many labs of the world.

Superconducting helmet based on SQUIDS

The main question about any superconductor is why the resistance is zero. The answer is this: All electrons in the condensate behave coherently, i.e. as a single electron. They form a bound electronic cloud, or BCS macro-molecule of electrons. The electric charge of this cloud equals to the total number of electrons in the condensate. The whole electronic molecule moves according to the Schrodinger equation. This quantum cloud can not leave the sample since it is stabilized by the ionic lattice of the material. Yet within the sample it moves according to the laws of Heisenberg quantum mechanics, i.e. it moves with zero friction.

Consider a single electron again. If it is placed on a wire loop, and a magnetic field is applied perpendicular to the loop, then the magnetic vector-potential is not zero inside the loop. According to the Schrodinger equation, the velocity of the electron is proportional to this vector-potential. In a superconductor all electrons form the BCS bound molecule and move as a whole. In other words they act coherently. The magnetic vector potential define the velocity of the BCS condensate and causes the Meissner effect to occur, due to induced currents,

One interesting parallel to the coherence of the electrons in the condensate is a laser. In the laser the photons behave coherently. Thus the light could be considered, at least on a qualitative level, as a condensate of photons. One objection to this could be that an attraction among the electrons is needed to form a superconducting BCS condensate. Yet, there is no attraction between photons. So, a critic might say, they could not form a condensate. Yet, let us not forget about the optically active medium of the laser. Their electrons produce new electrons due to photon-induced coherent emission from the excited atoms. So, in some sense one can view this as attraction, since if one electron is present, it “attracts” or gives birth to new ones.

It gets more exciting if the BCS condensate concept is applied living things. Consider a body of a person. It is made of a very large number of cells. The cells attract each other and they act coherently. Why, you might ask? Well because if a person goes somewhere then all cells collaborate and go together, as an ensemble. In this model the consciousness is the quantum-mechanical wavefunction of the condensate of cells. Like there is one microscopic wavefunction describing the entire condensate, so there is just one consciousness which describes the behavior of the condensate of cells, i.e. living organism. In superconductivity not all electrons are included in the BCS condensate, but there are stray electrons, which are called bogoliubons. So in the world of living organisms, not all cells take part in the multi-cell organisms. There are single-cell organism as well, which are analogous to bogoliubons.

If a superconducting wire loop is broken in two spots, one get a superconducting quantum interference device. It is the most sensitive device for detecting extremely weak magnetic fields. It is amazing but it is a fact that squids can detected magnetic field generated by the brain of a person, when the person starts to think about something. The picture shows one such helmet with SQUIDs, which is able to read the thoughts. This is scary of course, since this technology breaks the privacy of thoughts.

History of Superconductivity.

For almost 50 years, the heavyweights of physics brooded over the puzzle. Then, 50 years ago last month, the answer appeared in the journal Physical Review. It was titled, simply, “Theory of Superconductivity.”

“It’s certainly one of the greatest achievements in physics in the second half of the 20th century,” said Malcolm R. Beasley, a professor of applied physics at Stanford.
Superconductivity was discovered in 1911 by a Dutch physicist, Heike Kamerlingh Onnes. He observed that when mercury was cooled to below minus-452 degrees Fahrenheit, about 7 degrees above absolute zero, electrical resistance suddenly disappeared, and mercury was a superconductor.
For physicists, that was astounding, almost like happening upon a real-world perpetual motion machine. Indeed, an electrical current running around a ring of mercury at 7 degrees above absolute zero would, in principle, run forever.
If the phenomenon defied intuition, it also defied explanation.
After wrapping up special and general relativity, Albert Einstein tried, and failed, to devise a theory of superconductivity. Werner Heisenberg, the physicist who came up with the Heisenberg uncertainty principle, struggled with the problem, as did other pioneers of quantum mechanics like Niels Bohr and Wolfgang Pauli. Felix Bloch, another thwarted theorist, jokingly concluded: Every theory of superconductivity can be disproved.
This long list of failure was unknown to Leon N. Cooper. In 1955 he had just received his Ph.D. and was working in a different area of theoretical physics at the Institute for Advanced Study in Princeton when he met John Bardeen, a physicist who had already won fame for the invention of the transistor.
Bardeen, who had left his transistor research at Bell Labs for the University of Illinois, wanted to recruit Dr. Cooper for his latest grand research endeavor: solving superconductivity.
“I talked to John for a while,” Dr. Cooper recalled at a conference in October, “and he said, ‘You know, it’s a very interesting problem.’ I said, ‘I don’t know much about it.’ He said, ‘I’ll teach you.’
“He omitted to mention,” Dr. Cooper said, “that practically every famous physicist of the 20th century had worked on the problem and failed.”
Bardeen himself had already made two unsuccessful assaults. Dr. Cooper said the omission was fortunate, because “I might have hesitated.”
Dr. Cooper arrived at the University of Illinois in September 1955. In less than two years, he, Bardeen and J. Robert Schrieffer, a graduate student, solved the intractable puzzle. Their answer is now known as B.C.S. theory after the initials of their last names.
Bardeen died in 1991, but Dr. Cooper and Dr. Schrieffer returned to the University of Illinois in October to commemorate the publication of their superconductivity paper.
Their Herculean achievement was honored with the 1972 Nobel Prize in physics, and it deeply influenced theorists who were putting together theories explaining the to and fro of fundamental particles. The theory has also been applied in subjects as far flung as the dynamics of neutron stars.
B.C.S. theory, however, never achieved recognition in popular culture like relativity and quantum mechanics. That may be understandable given the theory’s complexities, applying quantum mechanics to the collective behavior of millions and millions of electrons. “They were very, very difficult calculations,” Dr. Cooper recalled. “They were superdifficult.”
Even for physicists, the 1957 paper was a difficult one to read.
On the first day of the October conference, Vinay Ambegaokar of Cornell held up a small notebook from 1958. The notebook, Dr. Ambegaokar said, “shows I read it, but I did not understand it.” He said that he continued to prefer approaches “with less constant intellectual effort.” (Soviet physicists had come up with a so-called phenomenological theory — equations that described the behavior of superconductors but did not explain what created that behavior.)
Electrical resistance arises because the electrons that carry current bounce off the nuclei of the atoms, like balls in a diminutive pinball machine. The nuclei recoil and vibrate, sapping energy from the electrons.
In a superconductor, electrons seem more like ghosts than particles, passing the nuclei as if they were not there.
Clues to the nature of superconductivity began to accumulate when Walther Meissner and Robert Ochsenfeld, two German physicists, measured the magnetic field inside a superconductor and discovered, to everyone’s surprise, that it was exactly, precisely zero. Further, any magnetic field that was present in a material would disappear as it was cooled into a superconductor.
This phenomenon, known as the Meissner Effect, was the first sign that superconductors were more than just the perfect conductors envisioned in the early theories.
Then there were signs of a large energy gap between the lowest energy, superconducting state and the next possible, higher-energy configuration. That kept the electrons trapped in the superconducting state.
Finally, experiments showed that the temperature at which an electrical resistance disappeared varied when heavier or lighter versions of an atom were substituted; the weight of atoms play a negligible role in the electrical resistance of ordinary conductors.
Bardeen believed that if he could understand the energy gap, he would understand superconductivity.
In 1955, David Pines — Dr. Schrieffer’s predecessor in the Bardeen group — came up with the first breakthrough.
Negatively charged electrons generally repulse each other, but Dr. Pines showed that vibrations in the lattice of nuclei could generate a minuscule attraction.
When an electron passes near a positively charged atomic nucleus, the opposite electric charge slightly pulls the nucleus toward the electron. The electron flits away, leaving behind a positively charged wake, and that, in turn, attracts other electrons.
Dr. Pines’s result showed why the weight of the atoms mattered — heavier atoms accelerate more slowly.
The next two key breakthroughs came via mass transit.
In December 1956, Dr. Cooper was on a 17-hour train ride to New York City. He had spent his first months applying his theoretical bag of tricks on the equations. “I did it and I did it and I did it, and I got absolutely nowhere,” he said. “I wasn’t feeling that clever any more.”
On the train, Dr. Cooper discarded his failed calculations. “I just thought and thought, ‘I know this is a difficult problem, but it seems so simple,’” he said. Physicists think of electrons in a normal conductor as piling on top of one another in a “Fermi sea,” named after Enrico Fermi, who was still formulating the theory at the University of Chicago.
Dr. Cooper realized that it was only the electrons near the top of the Fermi sea that were crucial. “You introduce a small effect,” he said, “and somehow you get a superconductor.”
As he worked on the problem for the next few months, Dr. Cooper realized that these electrons not only attracted others as Dr. Pines had shown, but also grouped themselves into pairs. It now seemed that superconductivity depended on these pairs, subsequently named Cooper pairs.
Contrary to simple expectations, the two electrons did not revolve closely around each other but were far apart, with many other electrons in between. The multitude of overlapping pairs made the calculations a morass.
A year after Dr. Cooper’s trip, Dr. Schrieffer headed to New York for a scientific conference. (At the same time, Bardeen headed to Stockholm to collect his first Nobel Prize, for the transistor.) Dr. Schrieffer had been looking at statistical approaches to solve the tangle of Cooper pairs. On the subway, he wrote down the answer, which turned out to be fairly simple in form.
The Cooper pairs essentially coalesced into one large clump that moved together, and the energy gap prevented the scattering of any one pair. Dr. Schrieffer gives the analogy of a line of ice skaters, arm in arm. “If one skater hits a bump,” he said, the skater is “supported by all the other skaters moving along with it.”
Back in Illinois, he showed what he had written to Dr. Cooper and then Bardeen. Bardeen was convinced.
Charles P. Slichter, a professor of physics at Illinois then and now and who had conducted many of the experiments teasing out the clues to superconductivity, remembered Bardeen’s stopping him in the hallway one day.
“John wasn’t a great talker,” Dr. Slichter said. “I could see he had something he wanted to say, and we sort of stood there. It seemed like we stood there for five minutes.”
Dr. Slichter was tempted to say something, “but I knew I shouldn’t, because if I did, I would shut him up. So he spoke to me finally. ‘Well, Charlie, I think we’ve solved superconductivity.’
“And wow, it is the most exciting moment in science I’ve ever experienced,” Dr. Slichter said.
In February 1957, the three submitted a paper, essentially outlining their ideas, to Physical Review. Their longer, more complete paper did not appear in print until December that year.
A new puzzle appeared in 1986 with the discovery of so-called high-temperature superconductors. These superconductors work at higher, though still very low, temperatures.
No theory has emerged as convincing; one session at the Illinois conference was a mass interrogation of the competing theorists.
The theorists agreed that high-temperature superconductors were different, that the attractive force did not come from the vibrations of nuclei. Rather, they said, the attraction somehow arose from the flipping of the atoms’ tiny magnetic poles. Beyond that, they did not agree.
Other types of superconductors, and more theories, could well follow.
As Dr. Beasley of Stanford said in the closing talk of the conference: “We have no idea of the limits of superconductivity in the universe. If 85 percent of the universe is dark matter, I hope 5 percent of it is superconducting.”

Critical temperatures of common superconductors:
Aluminum: 1.2 K
Gallium: 1.1K
Indium: 3.4 K
Lead: 7.2 K
Mercury: 4.2 K
Niobium: 9.3 K
Tin: 3.7 K
La-Ba-Cu-oxide: 17.9 K
Y-Ba-Cu-oxide: 92 K
Tl-Ba-Cu-oxide: 125 K

NbTi: 9.5-10.5 K
Nb3Sn: 18.1-18.5 K
NbN: 14.5-17.8 K

Single molecules can be used as perfect templates or scaffolds for metal deposition. 
For example, it is possible to decorate a single nanotube with a film of amorphous metal and produce a homogeneous nanowire of width in the range 5-10 nm.
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