8 Se p 20 06 Hall resistivity of granular metals

We calculate the Hall conductivity σxy and resistivity ρxy of a granular system at large tunneling conductance gT ≫ 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 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. The Coulomb interaction gives rise to logarithmic in temperature T correction to ρxy in the range Γ . T . min(gTEc, ETh), where Γ is the tunneling escape rate, Ec is the charging energy and ETh is the Thouless energy of the grain.