Hall Effect in Granular Metals: Weak Localization Corrections

We study the effects of localization on the Hall transport in a granular system at large tunneling conductance $g_T\gg 1$ corresponding to the metallic regime. We show that the first-order in 1/g_T weak localization correction to Hall resistivity of a two- or three-dimensional granular array vanishes identically, $\text{de}{\rho }_{xy}^{WL}=0$. This result is in agreement with the one for ordinary disordered metals. Being due to an exact cancellation, our result holds for arbitrary relevant values of temperature T and magnetic field H, both in the homogeneous'' regime of very low T and H corresponding to ordinary disordered metals and in the structure-dependent’’ regime of higher values of T or H.