Topological quantization and degeneracy in Josephson-junction arrays

We consider the conductivity quantization in two-dimensional arrays of mesoscopic Josephson junctions, and examine the associated degeneracy in various regimes of the system. The filling factor of the system may be controlled by the gate voltage as well as the magnetic field, and its appropriate value for quantization is obtained by employing the Jain hierarchy scheme both in the charge description and in the vortex description. The duality between the two descriptions then suggests the possibility that the system undergoes a change in degeneracy while the quantized conductivity remains fixed