Pairing, Magnetic Spin Fluctuations, and Superconductivity Near a Quantum Critical Point

The properties of a wide variety of intermetallic compounds exhibiting magnetic localized spin and superconducting fluctuations near a quantum critical point (QCP) are reviewed. They show highly anomalous critical indices (anomalously small). Laws of corresponding are observed in these materials and a theory is presented which gives a fully quantitative explanation of these laws. The theory employs a gauge transformation which rotates the electron spin quantization axis into the direction of the instantaneous staggered localized spin direction , where is the localized spin array wave vector. Many properties of these materials are worked out on the basis of this theory. The technological promise of these substances is truly immense, including energy generation, storage and transmission, MRI magnets, industrial and scientific magnets, maglev, cellular communications, -wave electronics, etc.