Dynamic Measurement of Percolative Critical Exponents in Disordered Josephson Junction Arrays

Abstract

The complex conductance $G(\ensuremath{\omega})$ of site-diluted Josephson junction arrays close to the percolation threshold was measured over a wide range of frequencies \ensuremath{\omega}. Well below ${T}_{c}$ both the superfluid $[\ensuremath{\omega}\mathrm{Im}G]$ and dissipative $[\mathrm{Re}G]$ components are independent of \ensuremath{\omega} below a critical frequency ${\ensuremath{\omega}}_{c}$, whereas $G(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}u}$ with $u\ensuremath{\approx}\frac{1}{2}$ for $\ensuremath{\omega}>{\ensuremath{\omega}}_{c}$. This is shown to reflect the crossover from a Euclidean regime $(\ensuremath{\omega}<{\ensuremath{\omega}}_{c})$ dominated by phononlike modes of the phase system to a fractal regime $(\ensuremath{\omega}>{\ensuremath{\omega}}_{c})$, where the relevant excitations are localized fractons. Percolative critical exponents extracted from the data are consistent with theoretical predictions.