Electron-hole Asymmetry and Quantum Critical Point in Hole-doped BaFe$_2$As$_2$

We show, from first-principles calculations, that the hole-doped side of FeAs-based compounds is different from its electron-doped counterparts. The electron side is characterized as Fermi surface nesting, and SDW-to-NM quantum critical point (QCP) is realized by doping. For the hole-doped side, on the other hand, orbital-selective partial orbital ordering develops together with checkboard antiferromagnetic (AF) ordering without lattice distortion. A unique SDW-to-AF QCP is achieved, and $J_2$=$J_1/2$ criteria (in the approximate $J_1&J_2$ model) is satisfied. The observed superconductivity is located in the vicinity of QCP for both sides.