Quantum phase transition in small-size one- and two-dimensional Josephson junction arrays: Analysis of experiments within the interacting plasmons picture

Theoretically, Josephson junction (JJ) arrays can exhibit either a superconducting or insulating state, separated by a quantum phase transition (QPT). In this work, we analyze published data in three one-dimensional arrays and two two-dimensional arrays using a recently developed phenomenological model of QPTs. The model is based on the insight that the scaled experimental data depend in a universal way on two characteristic length scales of the system: the microscopic length scale ${L}_{0}$ from which the renormalization group flow starts, and the dephasing length ${L}_{\ensuremath{\varphi}}(T)$ as given by the distance traveled by system-specific elementary excitations over the Planckian time. Our analysis reveals that the data for all five arrays (both 1D and 2D) can be quantitatively and self-consistently explained within the framework of interacting superconducting plasmons. In this picture, ${L}_{\ensuremath{\varphi}}={v}_{p}\ensuremath{\hbar}/{k}_{B}T$ and ${L}_{0}\ensuremath{\approx}\mathrm{\ensuremath{\Lambda}}$, where ${v}_{p}$ is the speed of the plasmons and $\mathrm{\ensuremath{\Lambda}}$ is the Coulomb screening length of the Cooper pairs. We also discuss similarities and differences with recent microwave studies of extremely long JJ chains, as well as with the pair-breaking QPT observed in superconducting nanowires and films.