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

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

2007-04-05

arxiv.org/abs/0704.0741v1

Phys. Rev. B 76, 094202 (2007)

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, RevTex4, 3 eps figures

Scientific paper

10.1103/PhysRevB.76.094202

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 $\Delta\sigma_\mathrm{WL}(L_\phi)$ 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.

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