Orbital ordering of complex orbitals in doped Mott insulators

Orbital ordering, often observed in Mott insulators with orbital degeneracy, is usually supposed to disappear with doping, e.g., in the ferromagnetic metallic phase of manganites. We propose that the orbital ordering of a novel type may exist in such a situation: there may occur an orbital ordering of complex orbitals (linear superposition of basic orbitals $d_{x^2-y^2}$ and $d_{z^2}$ with complex coefficients). Despite the perfect orbital ordering, such a state still retains cubic symmetry and thus would not induce any structural distortion. This state can resolve many problems in the physics of colossal magnetoresistance manganites and can also exist in other doped Mott insulators with Jahn-Teller ions.