Multiband superconductors under magnetic fields: Fractional vortices and Ising superconductivity

Inspired by the recent experiments in monolayer iron-based superconductors, we theoretically investigate the properties of a two-dimensional multiband superconductor under magnetic fields, focusing on two aspects. First, for vortex bound states under out-of-plane magnetic fields, the spatial anisotropy and positions of electron density peaks are associated with interband couplings. Second, under in-plane magnetic fields, even with inversion symmetry, a Ising-type spin-orbit coupling is allowed, leading to an enhanced in-plane upper critical field. Applications to other two-dimensional multiband superconductors are also discussed.