Mesoscopic charging effects in the $\sigma$-model for granular metals

Abstract

We derive the $\sigma$-model for granular metals. It is valid for any relation between the temperature, $T$, and the grain mean level spacing. The continuum limit of the $\sigma$-model describes non-perturbative charging effects in homogeneous disordered metals. The $\sigma$-model action contains a novel term which is crucial for studying Coulomb blockade effects. Topological properties of the $\sigma$-model encoding charge discreteness are studied. For $T$ below the escape rate from the grain, $\Gamma$, Coulomb blockade effects are described by solitons of the $Q$-matrix which are delocalized in real space. At $T>\Gamma$ the solitons transform into phase instantons localized at a single tunneling contact.

arXiv comment4 pages

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Cited by in corpus (6)

• Granular Electronic Systems
• Universal Description of Granular Metals at Low Temperatures: Granular Fermi Liquid
• Inelastic electron transport in granular arrays
• Suppression of superconductivity due to non-perturbative saddle points in the nonlinear $\sigma$-model
• Proximity effect in the presence of Coulomb interaction and magnetic field
• Nonperturbative interaction effects in the thermodynamics of disordered wires