Hall transport in granular metals

We present a theory of the Hall effect in dense-packed granular systems at large tunneling conductance g_T≫1 (metallic regime). The Hall transport is essentially determined by the intragrain electron dynamics which, as we find using the Kubo formula and diagrammatic technique, can be described by nonzero diffusion modes inside the grains. We show that in the absence of quantum effects the Hall resistivity ρ_xy depends neither on the tunneling conductance nor on the intragrain disorder and is given by the classical formula ρ_xy=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. We then study the quantum effects of the Coulomb interaction and weak localization by calculating the first order in 1/g_T corrections and find that (i) in a wide range of temperatures T≳Γ exceeding the tunneling escape rate Γ , the Coulomb interaction gives rise to the logarithmic-in- T correction to ρ_xy , which is of local origin and absent in conventional disordered metals; (ii) the large-scale “Altshuler-Aronov” correction to the Hall conductivity σ_xy vanishes, δσ_xy^AA=0 ; (iii) the weak localization correction to the Hall resistivity ρ_xy vanishes, δρ_xy^WL=0 . The results (ii) and (iii) are in agreement with the theory of conventional disordered metals.