Hall transport in granular metals

We present a theory of the Hall effect in dense-packed granular systems at large tunneling conductance gT⪢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 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. We then study the quantum effects of the Coulomb interaction and weak localization by calculating the first order in 1∕gT 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 ρxy, which is of local origin and absent in conventional disordered metals; (ii) the large-scale “Altshuler-Aronov” correction to the Hall conductivity σxy vanishes, δσxyAA=0; (iii) the weak localization correction to the Hall resistivity ρxy vanishes, δρxyWL=0. The results (ii) and (iii) are in agreement with the theory of conventional disordered metals.