| We present a theory of Hall effect in granular systems at large tunneling conductance gT>> 1. Hall transport is essentially determined by the intragrain electron dynamics, which can be described by nonzero diffusion modes inside the grains. We show that in the absence of quantum effects Hall resistivity ρxy depends neither on the tunneling conductance nor on the intragrain disorder and is given by the classical formula ρxy=H/(n* ec), where n* differs from the carrier density n inside the grains by a numerical coefficient determined by the shape of the grains and type of granular lattice. Further, we study quantum effects of Coulomb interaction and weak localization by calculating first-order in 1/gT corrections and find that (i) in a wide range of temperatures T ≥ Γ exceeding the tunneling escape rate Γ charging effects give rise to the logarithmic in T correction to ρxy, which is of local origin and absent in homogeneously disordered metals; (ii) the large-scale "Altshuler-Aronov" correction to Hall conductivity σxy, relevant at low temperatures T<<Γ, vanishes; (iii) the weak localization correction to Hall resistivity ρxy vanishes. Results (ii) and (iii) are in agreement with the theory of homogeneously disordered metals. |
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