Vortex structure in exponentially shaped Josephson junctions

We report the numerical calculations of the static vortex structure and critical curves in exponentially shaped long Josephson junctions for in-line and overlap geometries. Each solution of the corresponding boundary value problem is associated with the Sturm-Liouville problem whose minimal eigenvalue allows to make a conclusion about the stability of the vortex. The change in width of the junction leads to the renormalization of the magnetic flux in comparison to the case of a linear one-dimensional model. We study the influence of the model's parameters and, particularly, the shape parameter on the stability of the states of the magnetic flux. We compare the vortex structure and critical curves for the in-line and overlap geometries. Our numerically constructed critical curve of the Josephson junction matches well with the experimental one.Comment: 8 pages, 10 figures, NATO Advanced Research Workshop on "Vortex dynamics in superconductors and other complex systems" Yalta, Crimea, Ukraine, 13-17 September 200

Radiation induced oscillations of the Hall resistivity in two-dimensional electron systems

We consider the effect of microwave radiation on the Hall resistivity in two-dimension electron systems. It is shown that the photon-assisted impurity scattering of electrons can result in oscillatory dependences of both dissipative and Hall components of the conductivity and resistivity tensors on the ratio of radiation frequency to cyclotron frequency. The Hall resistivity can include a component induced by microwave radiation which is an even function of the magnetic field. The phase of the dissipative resistivity oscillations and the polarization dependence of their amplitude are compared with those of the Hall resistivity oscillations. The developed model can clarify the results of recent experimental observations of the radiation induced Hall effect.Comment: 4 pages, 1 figur