Universal resistance capacitance crossover in current-voltage characteristics for unshunted array of overdamped $Nb–AlOx–Nb$ Josephson junctions

We report on some unusual behavior of the measured current-voltage characteristics (CVC) in artificially prepared two-dimensional unshunted array of overdamped $Nb–AlOx–Nb$ Josephson junctions. The obtained nonlinear CVC are found to exhibit a pronounced (and practically temperature independent) crossover at some current $Icr=(1/2βC−1)IC$ from a resistance $R$ dominated state with $VR=RI2−IC2$ below $Icr$ to a capacitance $C$ dominated state with $VC=ℏ/4eCI−IC$ above $Icr$⁠. The origin of the observed behavior is discussed within a single-plaquette approximation assuming the conventional resistively shunted junction model with a finite capacitance and the Ambegaokar–Baratoff relation for the critical current of the single junction.