Why is it interesting?

Layman

First I will explain how superconductivity arises, and then turn to theprofound, and as it transpired inspirational, importance of hidden sym-metry in this case.

An electron moving through a lattice of positively charged ions experi-ences an electrical attraction, which causes a slight distortion of the lattice.As a bell continues to ring after having been struck, so the lattice’s distor-tion may persist for a short while after the electron has passed. A secondelectron coming through finds a distorted lattice, and interacts with it. Ifthe timing, speed, and spinning motions are right, the two interactionswith the lattice cause the electrons to attract one another magnetically.They act cooperatively, like a single particle where the two spins, or indi-vidual magnetism, of the constituent electrons have canceled out.

American Leon Cooper was the first to realize this possibility, in 1956,and since then these twins have been called “Cooper Pairs.”8 Their con-stituent electrons are fermions—particles with half-integer spins, whichin quantum mechanics act like cuckoos, where two in the same nest areforbidden. In a Cooper pair, the duo collectively has integer spin and actslike a boson.9 Bosons, by contrast, are like penguins, where large numberscooperate as a colony. Bosons can collect together into the lowest-possibleenergy state—an effect known as Bose-Einstein condensation, after thescientists whose work led to this phenomenon being understood. It ismanifested in weird phenomena such as the “superfluid” ability of liquidhelium to flow through narrow openings without friction and of super-conductivity. In superconductivity, the Cooper Pairs act like bosons,which in concert make a “Bose condensate.” An analogy of the difference between conventional conductors, whichhave resistance to the flow of current and become hot, and superconduc-tors, which offer no measurable resistance at all, is dancing in a wild night-club in contrast to what happens when a professional troupe performs aroutine onstage.10 On a packed floor at a nightclub, hundreds of individualdancers are vigorously jiving, waving their arms, rocking from side to side,and bumping into one another. This state is like that of electrons in ametal. To model the electric field, imagine the dance floor is tilted to one side, as on a cruise ship, which is listing slightly. The force of gravity willpush the dancers gently toward one side of the room. As they drift across,they continue dancing, the whole ensemble behaving quite chaotically.The more collisions you have, the more energy you waste.

This is how electrons behave in a warm metal when an electric fieldpushes them in one direction. The electrons move in the direction dic-tated by the field, meanwhile bumping into one another, losing energy asheat. An overall movement of dancers—in this case electric charge—en-sues; electric current flows, but there is a lot of resistance along the way.

The Cooper Pairs in a superconductor are like professional ballroomdancers who are performing as a troupe, rather than as individual pairs.However, in this particular routine, your partner is not dancing with youcheek to cheek, but instead is far across the room, their motion mirroringyour own precisely. A large number of dancers may be between you andyour partner, each of them in turn being paired with another, somewherein the crowd. The entire company performs as a coherent whole, a senseof order existing throughout the ballroom.

Any disturbance that would hinder a single dancer in the first examplewould have to affect the full ensemble of performers in the second case.The collective power of the organized troupe enables it to continue unim-peded; their motion—the electric current for the real case of electrons—loses no energy.

All that is required for this to happen is the existence of the organizedpairs. The dynamics of the choreography will determine precisely howthey go about it, but the concept itself depends only on the ability of theelectrons to pair off. Today we know that this powerful pair bonding is anexample of spontaneous symmetry breaking; the symmetry that has be-come hidden in the real case of electrons in a superconductor is gauge in-variance of electromagnetism. This work would lead to two Nobel Prizes.

Nambu appears to have been the first to recognize that gauge invariance does hold true in the BCS Theory but has become hidden. He had identified a profound truth: When the temperature gets cold enough, the fun-damental patterns of electromagnetism—gauge invariance—may be hid-den, as a result of which strange things happen, such as the appearance of the boson like Cooper Pairs. …. In a superconductor, the ground state contains Cooper Pairs. It costsenergy to break up any pair, liberating individual electrons. Once liberated,the electrons have higher energy, the difference from their original bond-ing in pairs being called the “energy gap.” The freed electrons receive this energy, which via E=mc2 makes them appear to have gained mass. This gave Nambu an idea: If the universe itself was like a superconductor, could the masses of particles arise by some analogous mechanism? from "The Infinity Puzzle" by Frank Close

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