| We develop a theory of collective Cooper-pair transport of one- and two-dimensional Josephson-junction arrays in the insulating state. We find an Arrhenius-like thermally activated behavior at moderate temperatures and the double-exponential temperature dependence at very low temperatures, reflecting formation of a superinsulator state. In this state the conductivity exhibits sharp voltage threshold behavior: it abruptly switches from zero to a finite value as the bias achieves the threshold. In a one-dimensional chain, both the activation energy and voltage threshold scale linearly with the length of the array. In a 2D array, the activation energy scales as logarithm of its size while the threshold voltage retains the linear dependence. We identify the superinsulating transition as a charge binding-unbinding Berezinskii-Kosterlitz-Thouless-like transition. |
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