Josephson coupling and plasma resonance in a vortex crystal

The authors consider the magnetic field dependence of the plasma resonance frequency in vortex crystal state. The authors found that low magnetic field induces a small correction to the plasma frequency proportional to the field. The slope of this linear field dependence is directly related to the average distance between the pancake vortices in the neighboring layers, wandering length. This length is determined by both Josephson and magnetic couplings between layers. At higher fields the Josephson coupling is suppressed collectively and is determined by elastic energy of the vortex lattice. Analyzing experimental data, they found that (1) the wandering length becomes comparable with the London penetration depth near {Tc}, (2) at small melting fields (< 20 G) the wandering length does not change much at the melting transition demonstrating existence of the line liquid phase in this field range, and (3) the self consistent theory of pancake fluctuations describes very well the field dependence of the Josephson plasma resonance frequency up to the melting point.