Incompressible quantum Hall states in Josephson-junction arrays

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Abstract
We have shown that the charges in two-dimensional arrays of small Josephson junctions form Laughlin incompressible states in a magnetic field, so that the charge density is fixed in finite intervals of external parameters. Thus the system resembles a two-dimensional electron gas in the quantum Hall regime. In contrast to the latter one, the system is shown to be equivalent to a Bose gas with a weak contact repulsive interaction. We present numerical results for the main plateau in the charge density and also a toy model that enables us to develop the picture of all plateaus.