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.
Thermodynamics and transport properties of resistance-shunted Josephson junctions are studied theoretically in the tight-binding limit E C / E J ≪1, where E C and E J are a charging energy and a Josephson coupling energy respectively. Based on a phenomenological harmonic-oscillator model, weak coupling region K = R Q / R ≪1 is analytically studied, where R and R Q = h /(2 e ) 2 are a shunt resistance and the quantum resistance. In addition to an effective bandwidth
2ℏΔeff, we find that this multi-level system genuinely has a novel crossover at lower energy
KℏΔeff below which the density of states becomes strongly degenerate. These two energy scales control the linear DC responses, optical responses, and nonlinear I - V characteristics. The lower energy crossover indicates the existence of a new class of strongly-correlated phenomena beyond the framework of the Kondo problem.