The modified London equation, Abrikosov-like vortices and knot solitons in two-gap superconductors

We derive the exact modified London equation for the two-gap superconductor, and compare it with its single-gap counterpart. We show that the vortices in the two-gap superconductor are soft (or continuous) core vortices. In particular, we discuss the topological structure of the finite-energy vortices (Abrikosov-like vortices), and find that they can be viewed as the incarnation of the baby skyrmion stretched in the third direction. Besides, we point out that the knot soliton in the two-gap superconductor is the twisted Abrikosov-like vortex with its two periodic ends connected smoothly. The relation between the magnetic monopoles and the Abrikosov-like vortices is also discussed briefly.