Hall Effect in Granular Metals: Weak Localization Corrections

TL;DR

This paper investigates how weak localization affects Hall resistivity in granular metals and finds that the first-order correction vanishes, aligning with behavior in ordinary disordered metals across various temperatures and magnetic fields.

Contribution

It demonstrates that the first-order weak localization correction to Hall resistivity in granular metals is zero, extending the understanding of localization effects to these systems.

Findings

First-order WL correction to Hall resistivity vanishes

Result holds for arbitrary T and H values

Agreement with behavior in ordinary disordered metals

Abstract

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, $\de \rho_{xy}^{WL}=0$. 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.