BYERS AND YANG'S THEOREM ON FLUX QUANTIZATION

In 1961 Byers and Yang have discovered a theorem of periodicity of energy levels in units of a flux quantum. In superconductors, the quantum unit is hc/2e. In the semiconductors, the pairing does not occur so that the flux quantum is hc/e. We show that Byers and Yang's flux quantization is applicable to the fractional charge, experimentally observed in the quantum Hall effect. It particularly explains the observation of 1/3 charge. The flux quantization also occurs for spin other than 1/2. We find that for spin 3/2 unusual series of large charges are predicted. The charge becomes very large such as 10e, 14e,., etc. For example, for S = 3/2, (1/2)g = (1/2)+s = 2 so that g = 4, and the factor (5/2)g becomes 10 which corresponds to the effective charge of 10e. The flux quantization gives rise to plateaus and energies become independent of magnetic field. Apparently, the problem becomes independent of charge and the plateaus are then quantized in units of h²/m, the square of the Planck's constant divided by the mass of the electron.

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