Quantum dynamics of in-plane Josephson junctions between two d-wave superconducting films is described by the anisotropic XY -model, where both quasiparticle and Cooper pair tunnelling terms appear to be equally non-local. Applying a combination of the weak and strong coupling analyses to this model, we find compelling evidence of a dissipative phase transition. The corresponding critical behaviour is studied and contrasted with that found previously in the conventional (s-wave) Josephson junctions.
Numerical identification of three distinct phases in a (2+1)D array of quantum dissipative Josephson junctions