an ordered, strongly correlated structure. The atoms in the lattice have outer electron shells that are almost exactly half-filled, so that there is one conduction electron per atom and the material is an insulator. Doping the material produces mobile holes. The collective behavior responsible for the transition to superconductivity occurs through correlations of the electron spins.

Another spin-polarization theory based on the Hubbard model pictures strong coupling of the electrons based on antiferromagnetic spin fluctuations. The charge carriers are holes—missing electrons—that are created as barium is added to lanthanum copper oxide. Cooper pairing occurs as a result of interactions between the spins of the holes and neighboring electrons.

One theory that aroused enthusiasm for a while was based on exotic particles called anyons or semions, which are neither bosons nor fermions, Haldane said. A pair of fermions can form a boson; so can a pair of bosons, he explained. In a two-dimensional system, there is a third possibility: Two semions can pair to form a boson, too. The anyon theory is that the boson sea of a high-temperature superconductor is formed by as-yet-undetected particles whose properties are halfway between those of fermions and bosons. The anyon theory requires time-reversal breaking—a violation of the rule that a movie made of a particle interaction would show the exact reverse of that interaction when run backward. Experiments done at Bell Laboratories in 1990 indicated that time reversal was violated in the new superconductors, a finding that gave prominence to the anyon theory. Interest has faded as other laboratories have failed to replicate the broken time-reversal studies, Haldane said.

Yet another theory assumes the existence of "soft" phonons associated with what is called a breathing mode, in which oxygen atoms that are around copper ions in the lattice move in and out regularly. As temperature drops, the breathing mode should soften—that is, oscillate at lower and lower frequencies. Below a given temperature, the oscillation stops. The resulting "frozen phonons" allow strong electron coupling that permits high transition temperatures.

Another theory posits interactions mediated by bipolarons. A polaron is an electron that sits in a pocket of positive charge in a lattice; a bipolaron is a pair of such electrons. Bipolarons can undergo a Bose condensation if the electron structure of a material meets certain conditions that can occur in layered materials such as the oxide superconductors.

Philip W. Anderson of Princeton University has proposed a resonance valence bond (RVB) theory that assumes no polarization of any kind. It postulates a spin liquid, in which electrons can be described



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