Hall resistivity of granular metals

We calculate the Hall conductivity ${\text{sig}}_{xy}$ and resistivity ${\rho }_{xy}$ of a granular system at large tunneling conductance $g_T\gg 1$. 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 ${\rho }_{xy}=H\mathrm{/}(n^{\ast }ec)$, where $n^{\ast }$ 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 ${\rho }_{xy}$ in the range $\Ga \lesssim T \lesssim \min(g_T E_c,\ETh)$,where$\Ga$isthetunnelingescaperate,$E_c$ is the charging energy and $\text{ETh}$ is the Thouless energy of the grain.