Manifestation of geometric quantization effects in temperature behavior of AC magnetic response of Josephson Junction Arrays

By improving resolution of home-made mutual-inductance measurements technique, a pronounced step-like structure (with the number of steps n=4 for all AC fields) has been observed in the temperature dependence of AC susceptibility in artificially prepared two-dimensional Josephson Junction Arrays (2D-JJA) of unshunted Nb-AlO_x-Nb junctions with \beta_L(4.2K)=30. Using a single-plaquette approximation of the overdamped 2D-JJA model, we were able to successfully fit our data assuming that steps are related to the geometric properties of the plaquette. The number of steps n corresponds to the number of flux quanta that can be screened by the maximum critical current of the junctions. The steps are predicted to manifest themselves in arrays with the inductance related parameter \beta_L(T) matching a "quantization" condition \beta_L(0)=2\pi (n+1).