In the electron-phonon interaction of the BCS theory, the electron polarizes the lattice. Two other things can be polarized, charge or spin. A huge variety of exotic polarizing mechanisms—excitons, plasmons, spin fluctuations—have been proposed.

A theory based on charge polarization postulates the excitonic mechanism, first outlined by Vitaly Ginzburg of the Soviet Union and independently by William Little of Stanford University and later developed by Bardeen, David Allender, and James Bray at the University of Illinois. It pictures electrons as being paired by exchange of a virtual particle, the exciton, that comes into existence when an electron moves to a higher energy state, creating a hole, and then drops back to the lower energy state. It can be put in another way: the electron creates a polarization cloud by pushing nearby electrons away because of the Coulomb repulsion between similarly charged particles. A second electron has its energy lowered because of the polarization cloud and forms a pair with the first. One problem with the excitonic mechanism is that it predicts transition temperatures that are too high—by hundreds or even thousands of kelvins. In addition, the requisite excitations have not been observed.

A spin-polarization theory first developed by P.-G. de Gennes assumes the production of virtual particles called magnons. It starts with a nonsuperconducting material in the antiferromagnetic state, in which neighboring electrons have spins of opposite orientation. When the material is doped by the addition of another element, holes are created that also carry a spin. Each hole wants to spin antiparallel to the electrons, but it also wants to delocalize—spread its wave function to other sites. But it sees antiferromagnetic electrons whose spins are aligned parallel with it at these other sites. Its spin is tilted, so that the electron can delocalize to some degree and still have a favorable alignment of its spin with the antiferromagnetic electrons. This causes a spin polarization cloud to form, attracting a second electron and forming a pair. The interaction is mediated by polarizing spin degrees of freedom.

The charge-polarization and spin-polarization theories are based on two sharply different pictures of the electron structure of the material. BCS theory assumes that the conduction electrons that form a Cooper pair are delocalized and move relatively independently. Charge-polarization theories also are based on this structure. Many spin-polarization theories assume a strikingly different structure, called the Mott-Hubbard insulator.

As described by Sir Nevill Mott, a British Nobel laureate in physics, and John Hubbard, a Briton who was with IBM before his death, the Mott-Hubbard insulator picture assumes that the electrons are in



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