Hall resistivity of granular metals

Details Hall resistivity of granular metals Hall resistivity of granular metals

2006-09-28

arxiv.org/abs/cond-mat/0609736v1

Phys. Rev. Lett. 99, 056803 (2007)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 1 figure

Scientific paper

10.1103/PhysRevLett.99.056803

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.

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