Renormalization-group study of gate charge effects in Josephson-junction   chains
  We study the quantum phase transition in a chain of superconducting grains, coupled by Josephson junctions, with emphasis on the effects of gate charges induced on the grains. At zero temperature the system is mapped onto a two-dimensional classical Coulomb gas, where the gate charge plays the role of an imaginary electric field. Such a field is found relevant in the renormalization-group transformation and to change the nature of the superconductor-insulator transition present in the system, tending to suppress quantum fluctuations and helping establish superconductivity. On the basis of this observation, we propose the zero-temperature phase diagram on the plane of the gate charge and the energy ratio. 
M.Y. Choi, Sung Wu Rhee, Minchul Lee, J. Choi