Valence transition model of the pseudogap, charge order, and superconductivity in electron-doped and hole-doped copper oxides

We present a valence transition model for electron- and hole-doped cuprates, within which there occurs a discrete jump in ionicity ${\mathrm{Cu}}^{2+}\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}{\mathrm{Cu}}^{1+}$ in both families upon doping, at or near optimal doping in the conventionally prepared electron-doped compounds and at the pseudogap phase transition in the hole-doped materials. In thin films of the ${\mathrm{T}}^{\ensuremath{'}}$ compounds, the valence transition has occurred already in the undoped state. The phenomenology of the valence transition is closely related to that of the neutral-to-ionic transition in mixed-stack organic charge-transfer solids. Doped cuprates have negative charge-transfer gaps, just as rare-earth nickelates and ${\mathrm{BaBiO}}_{3}$. The unusually high ionization energy of the closed shell ${\mathrm{Cu}}^{1+}$ ion, taken together with the doping-driven reduction in three-dimensional Madelung energy and gain in two-dimensional delocalization energy in the negative charge transfer gap state drives the transition in the cuprates. The combined effects of strong correlations and small $d\ensuremath{-}p$ electron hoppings ensure that the systems behave as effective 1/2-filled Cu band with the closed shell electronically inactive ${\mathrm{O}}^{2\ensuremath{-}}$ ions in the undoped state, and as correlated two-dimensional geometrically frustrated 1/4-filled oxygen hole band, now with electronically inactive closed-shell ${\mathrm{Cu}}^{1+}$ ions, in the doped state. The model thus gives microscopic justification for the two-fluid models suggested by many authors. The theory gives the simplest yet most comprehensive understanding of experiments in the normal states. The robust commensurate antiferromagnetism in the conventional ${T}^{\ensuremath{'}}$ crystals, the strong role of oxygen deficiency in driving superconductivity and charge carrier sign corresponding to holes at optimal doping are all manifestations of the same quantum state. In the hole-doped pseudogapped state, there occurs a biaxial commensurate period 4 charge density wave state consisting of ${\mathrm{O}}^{1\ensuremath{-}}\ensuremath{-}{\mathrm{Cu}}^{1+}\ensuremath{-}{\mathrm{O}}^{1\ensuremath{-}}$ spin singlets that coexists with broken rotational ${\mathrm{C}}_{4}$ symmetry due to intraunit cell oxygen inequivalence. Finite domains of this broken symmetry state will exhibit two-dimensional chirality and the polar Kerr effect. Superconductivity within the model results from a destabilization of the 1/4-filled band paired Wigner crystal [Phys. Rev. B 93, 165110 (2016) and Phys. Rev. B 93, 205111 (2016)]. We posit that a similar valence transition, ${\mathrm{Ir}}^{4+}\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}{\mathrm{Ir}}^{3+}$, occurs upon electron doping ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$. We make testable experimental predictions in cuprates including superoxygenated ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4+\ensuremath{\delta}}$ and iridates. Finally, as indirect evidence for the valence bond theory of superconductivity proposed here, we note that there exist an unusually large number of unconventional superconductors that exhibit superconductivity proximate to exotic charge ordered states, whose band fillings are universally 1/4 or 3/4, exactly where the paired Wigner crystal is most stable.