Phenomenological theory of cuprate superconductivity

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Reasonably good agreement with the superconducting transition temperatures of the cuprate high-Tc superconductors can be obtained on the basis of an approximate phenomenological theory. In this theory, two criteria are used to calculate the superconducting transition temperature. One is that the quantum wavelength is of the order of the electron-pair spacing. The other is that a very small fraction of the normal carriers exist as Cooper pairs at Tc. The resulting simple equation for Tc contains only two parameters: the normal carrier density and effective mass. We calculate specific transition temperatures for twelve cuprate superconductors.