Fractional quantization of Hall conductance

It is shown how the correlation energy of a system of two-dimensional electrons in a strong magnetic field may be enhanced if the electrons are in a regular array of the Landau orbitals. This gives an energy gap if the proportion of occupied orbitals is a simple fraction without giving rise to charge-density waves which may pin the system. The gap is determined self-consistently. Such a state can give rise to the plateaus in the Hall conductance observed at fractional multiples of e^{2}h.