The out of plane a.c. fluctuation conductivity of superconductor under magnetic field

The time-dependent Ginzburg-Landau model with thermal noise is used to calculate the out of plane a.c. fluctuation conductivity of type-II superconductor under magnetic field. We assume that thermal fluctuations, represented by the Langevin white noise, are strong enough to melt the Abrikosov vortex lattice created by the magnetic field into a moving vortex liquid. The nonlinear interaction term in the time-dependent Ginzburg-Landau equation is treated within the self-consistent Gaussian approximation. The real and imaginary parts of the out of plane a.c. fluctuation conductivity formula are summation over all Landau levels to treat arbitrary magnetic fields. Our results indicate that high frequencies can be effectively used to suppress the out-of-plane a.c. fluctuation conductivity in high-temperature superconductors. The results also have refined analytical form and are fitted well to experimental data on high-Tc superconductor. The results in two-dimensional and three-dimensional limits are directly inferred from the corresponding result of the layered model.