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 fourfold axis, i.e., $H\parallel [001]$ in cubic Nb. The observed FLL transformation along $H_{\text{c2}}$ is almost perfectly explained without using 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 such morphologies, particularly the stability of the scalene triangle lattice attributed to the lack of mirror symmetry about the Fermi velocity maximum direction in k-space.