Coulomb blockade and quantum tunnelling in an array of metallic grains

doi:10.1088/0953-8984/16/28/008

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Journal of Physics: Condensed Matter

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Journal of Physics: Condensed Matter Volume 16 Number 28 Create an alert RSS this journal

V Tripathi et al 2004 J. Phys.: Condens. Matter 16 4867 doi:10.1088/0953-8984/16/28/008

Coulomb blockade and quantum tunnelling in an array of metallic grains

V Tripathi, M Turlakov and Y L Loh

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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 $g\gg 1$ , the conductivity σ in d dimensions decreases logarithmically with temperature ( $\sigma /\sigma_{0}\sim 1-\frac {1}{\pi gd}\ln (gE_{\mathrm {c}}/T)$ ) (Panyukov and Zaikin 1991 Phys. Rev. Lett. 67 3168, Goppert and Grabert 2000 Eur. Phys. J. B 16 687, Efetov and Tschersich 2002 Europhys. Lett. 59 114), while for $g\rightarrow 0$ , the conductivity shows simple activated behaviour ( $\sigma \sim \exp (-E_{\mathrm {c}}/T)$ ). We show, for bare tunnelling conductance $g \gtrsim 1$ , that the parameter $\gamma \equiv g(1-2/(g\pi)\ln (gE_{\mathrm {c}}/T))$ determines the competition between charging and tunnelling effects. At low enough temperatures in the regime $1\gtrsim \gamma \gg 1/\sqrt {\beta E_{\mathrm {c}}}$ , a charge is shared among a finite number $N=\sqrt { (E_{\mathrm {c}}/T)/\ln (\pi /2\gamma z)}$ of grains, and we find a soft activation behaviour of the conductivity, $\sigma \sim z^{-1}\exp (-2\sqrt {(E_{\mathrm {c}}/T)\ln (\pi /2\gamma z)})$ , where z is the effective coordination number of a grain.