The Relationship Between High-Temperature Superconductivity and the Fractional Quantum Hall Effect

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Science  28 Oct 1988:
Vol. 242, Issue 4878, pp. 525-533
DOI: 10.1126/science.242.4878.525


The case is made that the spin-liquid state of a Mott insulator, hypothesized to exist by Anderson and identified by him as the correct context for discussing high-temperature superconductors, occurs in these materials and exhibits the principles of fractional quantization identified in the fractional quantum Hall effect. The most important of these is that particles carrying a fraction of an elementary quantum number, in this case spin, attract one another by a powerful gauge force, which can lead to a new kind of superconductivity. The temperature scale for the superconductivity is set by an energy gap in the spin-wave spectrum, which is also the fundamental measure of how "liquid" the spins are.