Phase and charge re-entrant phase transitions in two capacitively coupled Josephson arrays with ultrasmall junctions

Abstract

We have studied the phase diagram of two capacitively coupled Josephson junction arrays with charging energy, Ec, and Josephson coupling energy, EJ. Our results are obtained using a path integral Quantum Monte Carlo algorithm. The parameter that quantifies the quantum fluctuations in the ith array is defined by αi≡Eci∕EJi. Depending on the value of αi, each independent array may be in the semiclassical or in the quantum regime: We find that thermal fluctuations are important when α≲1.5 and the quantum fluctuations dominate when 2.0≲α. Vortices are the dominant excitations in the semiclassical limit, while in the quantum regime the charge excitations are important. We have extensively studied the interplay between vortex and charge dominated individual array phases. The phase diagrams for each array as a function of temperature and interlayer capacitance were determined from results for their helicity modulus, Υ(α), and the inverse dielectric constant, ϵ−1(α). The two arrays are coupled via the capacitance Cinter at each site of the lattices. When one of the arrays is in the quantum regime and the other one is in the semiclassical limit, Υ(T,α) decreases with T, while ε−1(T,α) increases. This behavior is due to a duality relation between the two arrays: e.g., a manifestation of the gauge invariant capacitive interaction between vortices in the semiclassical array and charges in the quantum array. We find a re-entrant transition in Υ(T,α), at low temperatures, when one of the arrays is in the semiclassical limit (i.e., α1=0.5) and the quantum array has 2.0⩽α2⩽2.5, for the values considered for the interlayer capacitance of Cinter=0.26087, 0.52174, 0.78261, 1.04348, and 1.30435. Similar results were obtained for larger values of α2=4.0 with Cinter=1.04348 and 1.30435. For smaller values of Cinter the superconducting-normal transition was not present. In addition, when 3.0⩽α2<4.0, and for all the interlayer couplings considered above, a novel re-entrant phase transition occurs in the charge degrees of freedom, i.e., there is a re-entrant insulating-conducting transition at low temperatures. Finally, we obtain the corresponding phase diagrams that have some features that resemble those seen in experiment.

Similar papers