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

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.

Tilted and crossing vortex chains in layered superconductors

In the presence of the Josephson vortex lattice in layered superconductors, a small c-axis magnetic field penetrates in the form of vortex chains. In general, the structure of a single chain is determined by the ratio of the London [$\lambda$] and Josephson [$\lambda_{J}$] lengths, $\alpha= \lambda/\lambda_{J}$. The chain is composed of tilted vortices at large $\alpha$'s (tilted chain) and at small $\alpha$'s it consists of a crossing array of Josephson vortices and pancake-vortex stacks (crossing chain). We study chain structures at intermediate $\alpha$'s and found two types of phase transitions. For $\alpha\lesssim 0.6$ the ground state is given by the crossing chain in a wide range of pancake separations $a\gtrsim [2-3]\lambda_J$. However, due to attractive coupling between deformed pancake stacks, the equilibrium separation can not exceed some maximum value depending on the in-plane field and $\alpha$. The first phase transition takes place with decreasing pancake-stack separation $a$ at $a=[1-2]\lambda_{J}$, and rather wide range of the ratio $\alpha$, $0.4 \lesssim \alpha\lesssim 0.65$. With decreasing $a$, the crossing chain goes through intermediate strongly-deformed configurations and smoothly transforms into a tilted chain via a second-order phase transition. Another phase transition occurs at very small densities of pancake vortices, $a\sim [20-30]\lambda_J$, and only when $\alpha$ exceeds a certain critical value $\sim 0.5$. In this case a small c-axis field penetrates in the form of kinks. However, at very small concentration of kinks, the kinked chains are replaced with strongly deformed crossing chains via a first-order phase transition. This transition is accompanied by a very large jump in the pancake density.Comment: Proceeding of the NATO ARW "Vortex dynamics in superconductors and other complex systems", Yalta, Crimea, Ukraine, 13-17 September 2004, To be published in the Journ. of Low Temp. Phys., 16 pages, 6 figure

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