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

Abstract : We consider the correction ΔσeeΔσee 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 Δσee(LT)Δσee(LT) as a function of the thermal length LTLT is found very similar to the variation of the weak localization ΔσWL(Lϕ)ΔσWL(Lϕ) as a function of the phase coherence length. Our result for ΔσeeΔσee interpolates between the known 1d and 2d results, but the interaction parameter entering the expression of ΔσeeΔσee keeps a 1d behaviour. Quite surprisingly, the result is very close to the 2d logarithmic behaviour already for LT∼a/2LT∼a/2, where aa is the lattice parameter.

Christophe Texier 1 Gilles Montambaux 2
1 LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
2 LPS – Laboratoire de Physique des Solides