Parity Effect and Charge Binding Transition in Submicron Josephson Junction Arrays

TL;DR

This paper reexamines the BKT transition in Coulomb-dominated Josephson junction arrays, clarifying the conditions for the transition and explaining experimental observations of resistivity behavior.

Contribution

It demonstrates that the true phase transition occurs at a temperature T_1 = T_2/4, refining previous models and aligning theory with experimental data.

Findings

The BKT transition is a crossover, not a true phase transition, at T_2.

The actual transition occurs at T_1 = T_2/4.

The theory explains reentrant resistivity behavior in arrays.

Abstract

We reconsider the issue of Berezinskii-Kosterlitz-Thouless (BKT) transition into an insulating state in the Coulomb-dominated Josephson junction arrays. We show that previously predicted picture of the Cooper-pair BKT transtion at T = T_2 is valid only under the condition that T_2 is considerably below the parity-effect temperature (which is usually almost 10 times below the value of superconductive transition temperature), and even in this case it is not a rigorous phase transition but only a crossover, whereas the real phase transition takes place at T_1 = T_2/4. Our theory is in agreement with available experimental data on Coulomb-dominated Josephson arrays and also sheds some light on the origin of unusual reentrant temperature dependence of resistivity in the array with nearly-criticial ratio of Coulomb to Josephson energies.