Quantum phase transition in small-size 1d and 2d Josephson junction arrays: analysis of the experiments within the interacting plasmons picture

Abstract: Theoretically, Josephson junction (JJ) arrays can exhibit either a superconducting or insulating state, separated by a quantum phase transition (QPT). In this work, we analyzed published data on QPTs 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, $L_{\varphi}(T)$ as given by the distance travelled 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, $L_{\varphi}=v_p\hbar/k_B T$, and $L_0 \approx \Lambda$, where $v_p$ is the speed of the plasmons and $\Lambda$ is the Coulomb screening length of the Cooper pairs. We also observe that, in 1D arrays, the transition is significantly shifted towards the insulating side compared to the predictions of the sine-Gordon model. Finally, we 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.