Electronic state around vortex in a two-band superconductor

Based on the quasiclassical theory, we investigate the vortex state in a two-band superconductor with a small gap on a three-dimensional Fermi surface and a large gap on a quasi-two dimensional one, as in MgB₂. The field dependence of zero-energy density of states is compared for fields parallel and perpendicular to the ab plane, and the anisotropy of the vortex core shape is discussed for a parallel field. The Fermi surface geometry of two bands, combining the effect of the normal-like electronic state on the small gap band at high fields, produces characteristic behavior in the anisotropy of c and ab directions.