Granulated superconductors:from the nonlinear sigma model to the Bose-Hubbard description

Abstract

We modify a nonlinear sigma model (NLSM) for the description of a granulated disordered system in the presence of both the Coulomb repulsion and the Cooper pairing. We show that under certain controlled approximations this model is reduced to the Bose-Hubbard (or ``dirty-boson'') model with renormalized coupling constants. We obtain a more general effective action (which is still simpler than the full NLSM action) which can be applied in the region of parameters where the reduction to the Bose-Hubbard model is not justified. This action may lead to a different picture of the superconductor-insulator transition in 2D systems.

4 pages, revtex, no figures

References in corpus (5)

• Keldysh action for disordered superconductors
• Quantum interference and Coulomb interaction in arrays of tunnel junctions
• Fluctuation Conductivity in Insulator-Superconductor Transitions with Dissipation
• Observation of Critical Amplitude Fluctuations near the Two Dimensional Superconductor-Insulator Transition
• Nonlinear $\sigma$ model for disordered superconductors

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• Suppression of superconductivity due to non-perturbative saddle points in the nonlinear $\sigma$-model
• Superconducting Fluctuation Corrections to the Thermal Current in Granular Metals
• Realizing multiband states with ultracold dipolar quantum simulators
• Mesoscopic charging effects in the $\sigma$-model for granular metals
• BRST Invariant Theory Of A Generalized 1+1 Dimensional Nonlinear Sigma Model With Topological Term