Non-Abrikosov Vortex and Topological Knot in Two-gap Superconductor

We establish the existence of topologically stable knot in two-gap superconductor whose topology $\pi_3(S^2)$ is fixed by the Chern-Simon index of the electromagnetic potential. We present a helical magnetic vortex solution in Ginzburg-Landau theory of two-gap superconductor which has a non-vanishing condensate at the core, and identify the knot as a twisted magnetic vortex ring made of the helical vortex. We discuss how the knot can be constructed in the recent two-gap $\rm MgB_2$ superconductor.Comment: 4 pages, 3 figure

Bargmann-Wigner Formulation and Superradiance Problem of Bosons and Fermions in Kerr Space-time

The superradiance phenomena of massive bosons and fermions in the Kerr spacetime are studied in the Bargmann-Wigner formulation. In case of bi-spinor, the four independent components spinors correspond to the four bosonic freedom: one scalar and three vectors uniquely. The consistent description of the Bargmann-Wigner equations between fermions and bosons shows that the superradiance of the type with positive energy $(0<\omega)$ and negative momentum near horizon $(p_{\rm H}<0)$ is shown not to occur. On the other hand, the superradiance of the type with negative energy $(\omega<0)$ and positive momentum near horizon $(0<p_{\rm H})$ is still possible for both scalar bosons and spinor fermions