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Mesoscopic charging effects in the $σ$-model for granular metals

A. V. Andreev·I. S. Beloborodov
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Abstract

We derive the $σ$-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 $σ$-model describes non-perturbative charging effects in homogeneous disordered metals. The $σ$-model action contains a novel term which is crucial for studying Coulomb blockade effects. Topological properties of the $σ$-model encoding charge discreteness are studied. For $T$ below the escape rate from the grain, $Γ$, Coulomb blockade effects are described by solitons of the $Q$-matrix which are delocalized in real space. At $T> Γ$ the solitons transform into phase instantons localized at a single tunneling contact.

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A. V. Andreev, I. S. Beloborodov. 2003-08-13. Mesoscopic charging effects in the $σ$-model for granular metals. https://doi.org/10.1103/physrevb.69.081406

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