Hall resistivity of granular metals

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 ${\rho }_{xy}=H/(n^{\ast }ec)$, 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 $\Ga$ is the tunneling escape rate, $E_c$ is the charging energy and $\ETh$ is the Thouless energy of the grain.

4 pages, 1 figure

Cited by in corpus (1)

• Hall Transport in Granular Metals and Effects of Coulomb Interactions