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