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

Abstract

We consider the correction $\Delta {\sigma }_{\mathrm{ee}}$ 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 $\Delta {\sigma }_{\mathrm{ee}}(L_T)$ as a function of the thermal length $L_T$ is found very similar to the variation of the weak localization $\Delta {\sigma }_{\mathrm{WL}}(L_{\varphi })$ as a function of the phase coherence length. Our result for $\Delta {\sigma }_{\mathrm{ee}}$ interpolates between the known 1d and 2d results, but the interaction parameter entering the expression of $\Delta {\sigma }_{\mathrm{ee}}$ 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.

arXiv comment6 pages, RevTex4, 3 eps figures

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• Four-terminal resistances in mesoscopic networks of metallic wires: Weak localisation and correlations