The phase diagram of quantum disordered superconducting networks

Abstract

I review the low energy dynamics and the phase diagram of two parallel coupled Josephson junction arrays (JJA) in the presence of charge and magnetic frustration. Starting from the quantum phase model known to capture the relevant physics of JJA, the system is mapped in the self-dual limit into an Abelian gauge theory with a mixed Chern-Simons term. The low energy dynamics is shown to be governed by Higgs fields associated with disordering effects due to electric charges and magnetic excitations minimally coupled to gauge fields related to the currents of Cooper pairs and vortices. A rich phase diagram not attainable by standard mean field theories emerges as a result of the condensation of disorder fields. The interplay between Hall quantization and interlayer coherence displays appealing features resulting into quantized Hall states coexisting with interlayer coherence, quantized Hall states without interlayer coherence, and interlayer coherent states without Hall quantization.