Origin of spontaneous broken mirror symmetry of vortex lattices in Nb
  Combining the microscopic Eilenberger theory with the first principles band calculation, we investigate the stable flux line lattice (FLL) for a field applied to the four-fold axis; $H\parallel [001]$ in cubic Nb. The observed FLL transformation along $H_{c2}$ is almost perfectly explained without adjustable parameter, including the tilted square, scalene triangle with broken mirror symmetry, and isosceles triangle lattices upon increasing $T$. We construct a minimum Fermi surface model to understand those morphologies, in particular the stability of the scalene triangle lattice attributed to the lack of the mirror symmetry about the Fermi velocity maximum direction in k-space. 
H. M. Adachi, M. Ishikawa, T. Hirano, M. Ichioka, K. Machida
cond-mat.supr-con