Generic First Order Orientation Transition of Vortex Lattices in Type II Superconductors

First order transition of vortex lattices (VL) observed in various superconductors with four-fold symmetry is explained microscopically by quasi-classical Eilenberger theory combined with nonlocal London theory. This transition is intrinsic in the generic successive VL phase transition due to either gap or Fermi velocity anisotropies. This is also suggested by the electronic states around vortices. Ultimate origin of this phenomenon is attributed to some what hidden frustrations of a spontaneous symmetry broken hexagonal VL on the underlying four-fold crystalline symmetry.