Granular superconductors: From the nonlinear sigma model to the Bose-Hubbard description - art. no. 054515

We modify a nonlinear sigma model (NT sigmaM) for the description of a gran ular disordered system in the presence of both the Coulomb repulsion and th e Cooper pairing. We show that under certain controlled approximations the action of this model is reduced to the Ambegaokar-Eckern-Schon (AES) action , which is further reduced to the Bose-Hubbard (or "dirty-boson") model wit h renormalized coupling constants. We obtain an effective action which is m ore general than the AES one but still simpler than the full NL sigmaM acti on. This action can be applied in the region of parameters where the reduct ion to the AES or the Bose-Hubbard model is not justified. This action may lead to a different picture of the superconductor-insulator transition in t wo-dimensional systems.