Four-step scenario for doping-induced phase changes in a three-dimensional charge-density-wave system

A four-step scenario for the phase changes in Ba(1-x)KxBiO3 is proposed. This aims at giving a global view of the whole evolution process induced by hole doping. For this purpose, we utilize simple but standard methods such as the Hartree-Fock approximation and the adiabatic approximation. The parent material is BaBiO3, whose ground state is well established as a three-dimensional charge-density wave (CDW). While hole doping on this material is very light, we observe in the simulation that the hole bipolaron (BP) state is a local minimum with a higher energy than a pair of extended holes. We call this stage of doping the first step. Beyond a rather low critical concentration of holes, however, the second step emerges, where the BP state is stabilized as the lowest one. Moreover, upon continuing the doping, the system loses the initial long-range order of CDW and becomes disordered only with local CDW domains. The absorption spectrum in this third step shows a main band that moves to lower energies in accordance with the hole concentration. Lastly, at the final stage of doping, the pseudogap in the electronic density of states (DOS) collapses and the system becomes metallic. The aforementioned local CDW, however, still remains with reduced but finite fraction. Thus, this fourth step is characterized by a rather anomalous state of the metal. This scenario is qualitatively consistent with the experimental facts and gives a-reasonable description of the evolution of this material from very lightly doped states to heavily doped ones.