Plasma resonance at low magnetic fields as a probe of vortex line meandering in layered superconductors

We consider the magnetic field dependence of the plasma resonance frequency in pristine and in irradiated Bi$_2$Sr$_2$CaCu$_2$O$_8$ crystals near $T_c$. At low magnetic fields we relate linear in field corrections to the plasma frequency to the average distance between the pancake vortices in the neighboring layers (wandering length). We calculate the wandering length in the case of thermal wiggling of vortex lines, taking into account both Josephson and magnetic interlayer coupling of pancakes. Analyzing experimental data, we found that (i) the wandering length becomes comparable with the London penetration depth near T$_{c}$ and (ii) at small melting fields ($< 20$ G) the wandering length does not change much at the melting transition. This shows existence of the line liquid phase in this field range. We also found that pinning by columnar defects affects weakly the field dependence of the plasma resonance frequency near $T_c$.Comment: RevTex, 4 pages, 2 PS figures, Submitted to Phys. Rev.

Electrodynamics of Josephson vortex lattice in high-temperature superconductors

We studied 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 is inversely proportional to the anisotropy. The cases of weak and strong dissipation are realized in $\mathrm{Bi_{2}Sr_{2}CaCu_{2}O_{x}}$ and underdoped $\mathrm{YBa_{2}Cu_{3} O_{x}}$ correspondingly. The main feature of the response is the Josephson-plasma-resonance peak. In the weak-dissipation case additional satellites appear in the dilute regime mostly in the higher-frequency region due to excitation of the plasma modes with the wave vectors set by the lattice structure. In the dense-lattice limit the plasma peak moves to higher frequency and its intensity rapidly decreases, in agreement with experiment and analytical theory. 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 $\mathrm{YBa_{2}Cu_{3} O_{x}}$. It is caused by frequency dependence of in-plane contribution to losses rather then a definite mode of phase oscillations.Comment: 10 pages, 7 figures, to be published in Phys.Rev.B, supplementary animations of oscillating local electric field can be found at http://mti.msd.anl.gov/homepages/koshelev/projects/JPRinJVL/Nz2vc0_32vab6_0Anim.ht

Radiation Due to Josephson Oscillations in Layered Superconductors

We derive the power of direct radiation into free space induced by Josephson oscillations in intrinsic Josephson junctions of highly anisotropic layered superconductors. We consider the super-radiation regime for a crystal cut in the form of a thin slice parallel to the c-axis. We find that the radiation correction to the current-voltage characteristic in this regime depends only on crystal shape. We show that at large enough number of junctions oscillations are synchronized providing high radiation power and efficiency in the THz frequency range. We discuss crystal parameters and bias current optimal for radiation power and crystal cooling.Comment: 4 pages, 1 figure, to be published in Phys. Rev. Let

Josephson Coupling, Phase Correlations, and Josephson Plasma Resonance in Vortex Liquid Phase

Josephson plasma resonance has been introduced recently as a powerful tool to probe interlayer Josephson coupling in different regions of the vortex phase diagram in layered superconductors. In the liquid phase, the high temperature expansion with respect to the Josephson coupling connects the Josephson plasma frequency with the phase correlation function. This function, in turn, is directly related to the pair distribution function of the liquid. We develop a recipe to extract the phase and density correlation functions from the dependencies of the plasma resonance frequency $\omega_p({\bf B})$ and the $c$ axis conductivity $\sigma_c({\bf B})$ on the {\it ab}-component of the magnetic field at fixed {\it c} -component. Using Langevin dynamic simulations of two-dimensional vortex arrays we calculate density and phase correlation functions at different temperatures. Calculated phase correlations describe very well the experimental angular dependence of the plasma resonance field. We also demonstrate that in the case of weak damping in the liquid phase, broadening of the JPR line is caused mainly by random Josephson coupling arising from the density fluctuations of pancake vortices. In this case the JPR line has a universal shape, which is determined only by parameters of the superconductors and temperature.Comment: 22 pages, 6 figures, to appear in Phys. Rev. B, December