Hall Transport in Granular Metals and Effects of Coulomb Interactions

TL;DR

This paper develops a theoretical framework for understanding the Hall effect in granular metals with high tunneling conductance, highlighting the role of intragrain electron dynamics and Coulomb interactions in modifying Hall resistivity and conductivity.

Contribution

The paper introduces a detailed theory of Hall transport in granular systems, including first-order Coulomb interaction effects and their temperature dependence, extending previous models for disordered metals.

Findings

Hall resistivity is independent of tunneling conductance in the absence of interactions.

Coulomb interactions cause logarithmic temperature corrections to Hall resistivity and conductivity.

Large-scale Altshuler-Aronov corrections to Hall conductivity vanish at low temperatures.

Abstract

We present a theory of Hall effect in granular systems at large tunneling conductance $g_{T}\gg 1$. Hall transport is essentially determined by the intragrain electron dynamics, which, as we find using the Kubo formula and diagrammatic technique, can be described by nonzero diffusion modes inside the grains. We show that in the absence of Coulomb interaction the Hall resistivity $\rho_{xy}$ depends neither on the tunneling conductance nor on the intragrain disorder and is given by the classical formula $\rho_{xy}=H/(n^* e c)$, where $n^*$ differs from the carrier density $n$ inside the grains by a numerical coefficient determined by the shape of the grains and type of granular lattice. Further, we study the effects of Coulomb interactions by calculating first-order in $1/g_T$ corrections and find that (i) in a wide range of temperatures $T \gtrsim \Ga$ exceeding the tunneling escape rate $\Ga$, the Hall resistivity $\rho_{xy}$ and conductivity $\sig_{xy}$ acquire logarithmic in $T$ corrections, which are of local origin and absent in homogeneously disordered metals; (ii) large-scale ``Altshuler-Aronov'' correction to $\sig_{xy}$, relevant at $T\ll\Ga$, vanishes in agreement with the theory of homogeneously disordered metals.