Dipole magnetic flux in two-gap superconducting thin film in Ginzburg–Landau theory

•We develop the expression about vortex pair in two-gap superconducting thin film.•We study the possible dipole magnetic flux in vortex pair (I,+1) + (II,+1).•Two introduced parameters influence the flux structure of two-gap thin film.•The vortex pair (II,+1) + (II,−1) is important for thermal fluctuation.

In two-gap superconducting thin film, there are two kinds of pancake vortices: one is arisen from the vortex in the super-current of band I (it has greater gap) and the screening electrical current; another is arisen from the vortex in the super-current of band II and the screening electrical current. In London approximation, both carry fractional quantum magnetic flux ϕ01ϕ01 and ϕ02ϕ02 respectively. Except the change of the superconducting condensation energy in the region of pancake vortex, the energy of the pancake vortices include the magnetic energy and the Josephson type coupling energy between the Cooper pair of band I and II. Because the inter-bands Josephson coupling energy is infinite increase with the size of the film, the fractional magnetic flux cannot appear alone except in the boundary regions. The element for the investigation of the vortex in two-gap superconducting thin film is the pairs (I,s) + (II,s) and the pairs (II,+1) + (II,−1). We have discussed the magnetic interaction, the Josephson coupling interactions and the structure character of these pairs in this paper.