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

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

2003-08-13

arxiv.org/abs/cond-mat/0308254v1

Phys. Rev. B 69, 081406(R) (2004)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages

Scientific paper

10.1103/PhysRevB.69.081406

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.

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