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arXiv · 0704.0741

Al'tshuler-Aronov correction to the conductivity of a large metallic square network

Christophe Texier·Gilles Montambaux
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Abstract

We consider the correction $Δσ_\mathrm{ee}$ due to electron-electron interaction to the conductivity of a weakly disordered metal (Al'tshuler-Aronov correction). The correction is related to the spectral determinant of the Laplace operator. The case of a large square metallic network is considered. The variation of $Δσ_\mathrm{ee}(L_T)$ as a function of the thermal length $L_T$ is found very similar to the variation of the weak localization $Δσ_\mathrm{WL}(L_ϕ)$ as a function of the phase coherence length. Our result for $Δσ_\mathrm{ee}$ interpolates between the known 1d and 2d results, but the interaction parameter entering the expression of $Δσ_\mathrm{ee}$ keeps a 1d behaviour. Quite surprisingly, the result is very close to the 2d logarithmic behaviour already for $L_T\sim{a}/2$, where $a$ is the lattice parameter.

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Christophe Texier, Gilles Montambaux. 2007-04-05. Al'tshuler-Aronov correction to the conductivity of a large metallic square network. https://doi.org/10.1103/physrevb.76.094202

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