Coulomb blockade and quantum tunnelling in the low-conductivity phase of granular metals

Details Coulomb blockade and quantum tunnelling in the low-conductivity phase of granular metals Coulomb blockade and quantum tunnelling in the low-conductivity phase of granular metals

2003-07-22

arxiv.org/abs/cond-mat/0307534v3

J. Phys.: Condens. Matter 16, 4867 (2004)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

11 pages REVTeX, 3 Figures. Appendix added, replaced with published version

Scientific paper

10.1088/0953-8984/16/28/008

We study the effects of Coulomb interaction and inter-grain quantum tunnelling in an array of metallic grains using the phase-functional approach for temperatures $T$ well below the charging energy $E_{c}$ of individual grains yet large compared to the level spacing in the grains. When the inter-grain tunnelling conductance $g\gg1$, the conductivity $\sigma$ in $d$ dimensions decreases logarithmically with temperature ($\sigma/\sigma_{0}\sim1-\frac{1}{2\pi gd}\ln(gE_{c}/T)$), while for $g\to0$, the conductivity shows simple activated behaviour ($\sigma \sim \exp(-E_c/T)$). We show, for bare tunnelling conductance $g \gtrsim 1$, that the parameter $\gamma \equiv g(1-2/(g\pi)\ln(gE_{c}/T))$ determines the competition between charging and tunnelling effects. At low enough temperatures in the regime $1\gtrsim \gamma \gg 1/\sqrt{\beta E_{c}}$, a charge is shared among a finite number $N=\sqrt{(E_{c}/T)/\ln(\pi/2\gamma z)}$ of grains, and we find a soft activation behaviour of the conductivity, $\sigma\sim z^{-1}\exp(-2\sqrt{(E_{c}/T)\ln(\pi/2\gamma z)})$, where $z$ is the effective coordination number of a grain.

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