Electrodynamics of the Josephson vortex lattice in high-temperature superconductors

Abstract

We studied the response of the Josephson vortex lattice in layered superconductors to the high-frequency $c$-axis electric field. We found a simple relation connecting the dynamic dielectric constant with the perturbation of the superconducting phase, induced by oscillating electric field. Numerically solving equations for the oscillating phases, we computed the frequency dependences of the loss function at different magnetic fields, including regions of both dilute and dense Josephson vortex lattices. The overall behavior is mainly determined by the $c$-axis and in-plane dissipation parameters, which are inversely proportional to the anisotropy. The cases of weak and strong dissipations are realized in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{x}$ and underdoped $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{x}$, respectively. The main feature of the response is the Josephson-plasma-resonance peak. In the weak-dissipation case, additional satellites appear in the dilute regime in the higher-frequency region due to the excitation of the plasma modes with the wave vectors set by the lattice structure. In the dense-lattice limit, the plasma peak moves to a higher frequency, and its intensity rapidly decreases, in agreement with experiment and analytical theory. The behavior of the loss function at low frequencies is well described by the phenomenological theory of vortex oscillations. In the case of very strong in-plane dissipation, an additional peak in the loss function appears below the plasma frequency. Such peak has been observed experimentally in underdoped $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{x}$. It is caused by the frequency dependence of the in-plane contribution to losses rather than a definite mode of phase oscillations.