= Translation-symmetry breaking changes the band-filling constraint
A <band filling> constraint counts <electrons> per primitive <unit cell> of the actual translation symmetry. If an ordered state doubles the cell, a filling of one electron per original cell becomes two per new cell. The reduced <Brillouin zone> then permits reconstruction into different <energy bands>.
For spin-degenerate independent electrons, a filled band holds two electrons per primitive cell. Doubling can therefore remove the odd-filling obstruction to a <band insulator>, provided the reconstruction opens a global <band gap>. It does not guarantee a gap: folded bands can still overlap or retain symmetry-protected crossings. The original counting argument remains correct for its original symmetry assumptions; applying it after translation symmetry changes requires recounting using the new cell.
Back to article page
