Hall Resistivity of Granular Metals

We calculate the Hall conductivity σ_xy and resistivity ρ_xy of a granular system at large tunneling conductance g_T≫1. We show that in the absence of Coulomb interaction the Hall resistivity 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. The Coulomb interaction gives rise to logarithmic in temperature T correction to ρ_xy in the range Γ≲T≲min⁡(g_TE_c,E_Th), where Γ is the tunneling escape rate, E_c is the charging energy, and E_Th is the Thouless energy of the grain.