The stability of hole-doped antiferromagnetic state in a two-orbital model

We investigate the hole-doped antiferromagnetic state in a two-orbital model of cuprates. The model also includes $d_{3z^2-r^2}$ orbital. Unlike the one-orbital model, we find the antiferromagnetic state stable against the hole doping for the cuprates with orbital splitting between $d_{x^2-y^2}$ and $d_{3z^2-r^2}$ orbitals being ∼1 eV. This results from the fact that the Hund's coupling enforces the filling of $d_{x^2-y^2}$ orbital ≈1 indicated by a significant reduction of $d_{x^2-y^2}$ spectral density at the Fermi level. This, in turn, leads to the suppression of intraband fluctuations detrimental to the antiferromagnetic phase. In this scenario, hole doping involves removal of mainly $d_{3z^2-r^2}$ electrons that are comparatively more localized. One important caveat of our meanfield theoretic result and conclusion is that they are reliable only for a very low hole doping region. (paper)