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Abstract: We present a theory of Hall effect in granular systems at large tunnelingconductance $g {T}\gg 1$. Hall transport is essentially determined by theintragrain electron dynamics, which, as we find using the Kubo formula anddiagrammatic technique, can be described by nonzero diffusion modes inside thegrains. We show that in the absence of Coulomb interaction the Hall resistivity$ ho {xy}$ depends neither on the tunneling conductance nor on the intragraindisorder and is given by the classical formula $ ho {xy}=H-n^* e c$, where$n^*$ differs from the carrier density $n$ inside the grains by a numericalcoefficient determined by the shape of the grains and type of granular lattice.Further, we study the effects of Coulomb interactions by calculatingfirst-order in $1-g T$ corrections and find that i in a wide range oftemperatures $T \gtrsim \Ga$ exceeding the tunneling escape rate $\Ga$, theHall resistivity $ ho {xy}$ and conductivity $\sig {xy}$ acquire logarithmicin $T$ corrections, which are of local origin and absent in homogeneouslydisordered metals; ii large-scale ``Altshuler-Aronov- correction to$\sig {xy}$, relevant at $T\ll\Ga$, vanishes in agreement with the theory ofhomogeneously disordered metals.



Author: Maxim Yu. Kharitonov, Konstantin B. Efetov

Source: https://arxiv.org/







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