Hall resistivity of granular metals

TL;DR

This paper calculates the Hall resistivity of granular metals, showing it follows classical behavior without Coulomb interactions and identifying temperature-dependent corrections due to Coulomb effects.

Contribution

It provides a theoretical analysis of Hall resistivity in granular metals at high tunneling conductance, including Coulomb interaction effects and temperature dependence.

Findings

Hall resistivity follows classical formula in absence of Coulomb interactions.

Coulomb interactions introduce logarithmic temperature corrections.

Hall resistivity is independent of tunneling conductance and intragrain disorder in the non-interacting case.

Abstract

We calculate the Hall conductivity $\sig_{xy}$ 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 $\rho_{xy}=H/(n^* e c)$, where $n^*$ differs from the carrier density $n$ inside the grains by a numerical coefficient determined by the shape of the grains. 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 $\Ga$ is the tunneling escape rate, $E_c$ is the charging energy and $\ETh$ is the Thouless energy of the grain.