Ginzburg-Landau theory of vortices in a multigap superconductor

The Ginzburg-Landau functional for a two-gap superconductor is derived within the weak-coupling BCS model. The interaction between the two condensates is described by a unique Josephson-type mixing term. The two-gap Ginzburg-Landau theory is then applied to investigate various magnetic properties of ${\mathrm{MgB}}_2$ including an upturn temperature dependence of the transverse upper critical field and a core structure of an isolated vortex. The orientation of vortex lattice relative to crystallographic axes is studied for magnetic fields parallel to the c axis. A peculiar $30°$ rotation of the vortex lattice with increasing strength of an applied field observed by neutron scattering is attributed to the multigap nature of superconductivity in ${\mathrm{MgB}}_2.$