Charge-vortex duality in double-layered Josephson-junction arrays

A system of two parallel Josephson-junction arrays coupled by interlayer capacitances is considered in the situation where one layer is in the vortex-dominated and the other in the charge-dominated regime. This system shows a symmetry (duality) of the relevant degrees of freedom, i.e., the vortices in one layer and the charges in the other. In contrast to single-layer arrays both contribute to the kinetic energy. The charges feel the magnetic field created by vortices, and, vice versa, the vortices feel a gauge field created by charges. For long-range interaction of the charges the system exhibits two Berezinskii-Kosterlitz-Thouless transitions, one for vortices and another one for charges. The interlayer capacitance suppresses the temperature of vortex-unbinding transition. It further replaces the charge-unbinding transition by a crossover, which is strongly smeared already for weak interlayer coupling. The shift of the transition temperature for vortices is calculated in the quasiclassical approximation for arbitrary relations between the capacitances (both weak and strong coupling).