Theory of the valley-density wave and hidden order in iron pnictides

In the limit of perfect nesting, the physics of iron pnictides is governed by the density wave formation at the zone-edge vector M. At high energies, various spin-(SDW), charge-, and orbital/pocket-(PDW) density waves, and their linear combinations, all appear equally likely, unified within the unitary order parameter of U(4) x U(4) symmetry. Nesting imperfections and low-energy interactions reduce this symmetry to that of real materials. Nevertheless, the generic ground state preserves a distinct signature of its highly symmetric origins: A SDW along one axis of the iron lattice is predicted to coexist with a perpendicular PDW, accompanied by weak charge currents. This "hidden" order induces the structural transition in our theory, naturally insures T(s) >= T(N), and leads to orbital ferromagnetism and other observable consequences.