  To identify the contributions of the multiband nature and the anisotropy of a
microscopic electronic structure to a macroscopic vortex lattice morphology, we
develop a method based on the Eilenberger theory near Hc2 combined with the
first-principles band calculation to estimate the stable vortex lattice
configuration. For a typical two-band superconductor MgB2, successive
transitions of vortex lattice orientation that have been observed recently by
small angle neutron scattering [Das, et al.: Phys. Rev. Lett. 108 (2012)
167001] are explained by the characteristic field-dependence of twoband
superconductivity and the competition of sixfold anisotropy between the sigma-
and pi-bands. The reentrant transition at low temperature reflects the Fermi
velocity anisotropy of the sigma-band.
