Doping of charge density wave in ${\mathrm{Ba}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{K}}_{\mathrm{x}}$${\mathrm{BiO}}_3$

We study the formation of charge density waves (CDW) in ${\mathrm{Ba}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{K}}_{\mathrm{x}}$ ${\mathrm{BiO}}_3$ within a tight-binding model proposed by Prelovsek, Rice, and Zhang. Light doping leads to the formation of immobile bipolarons. The charge density wave amplitude diminishes gradually as doping concentration increases and disappears at about 35% doping. We have calculated the density of states and optical properties for various doping concentrations. We also present corresponding results in two dimensions that are applicable to a CDW system with the ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$ geometry.