Disorder in two-dimensional Josephson junctions

An effective free energy of a two-dimensional (i.e., large area) Josephson junction is derived, allowing for thermal fluctuations, random magnetic fields, and external currents. We show by using replica-symmetry-breaking methods that the junction has four distinct phases: disordered, Josephson ordered, a glass phase, and a coexisting Josephson order with the glass phase. Near the coexistence to glass transition at s= the critical current is ∼(area(Formula presented) where s is a measure of disorder. Our results may account for junction ordering at temperatures well below the critical temperature of the bulk in high-(Formula presented) trilayer junctions.