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.

arXiv comment4 pages, 1 figure

References in corpus (6)

• Granular Electronic Systems
• Quantum Effects in Coulomb Blockade
• Coulomb effects in granular materials at not very low temperatures
• Transport properties of granular metals at low temperatures
• Coulomb Zero-Bias Anomaly: A Semiclassical Calculation
• Transition from insulating to a non-insulating temperature dependence of the conductivity in granular metals

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• Electrical transport properties of thick and thin Ta-doped SnO${}_2$ films
• Scaling of the Hall effects beyond the quantum resistance threshold in oxidized CoFeB
• The granularity effect in amorphous InGaZnO${}_4$ films prepared by rf sputtering method
• Universal Hall coefficient correction in strongly coupled Cr-SiO${}_2$ nanogranular metals