Mesoscale Charge-Ordering in Transition Metal Oxides: Formation and Signatures

We briefly outline the value of an inhomogeneous (unrestricted) Hartree–Fock plus Random Phase approach for understanding the types and properties of mesoscopic patterns of localized small polarons in transition metal oxides. Using a multiband Peierls–Hubbard model for a hole-doped CuO2 layer as an illustrative example, we demonstrate the appearance of correlated high-energy (electronic) and low-energy (localized phonon and spin-wave) signatures of various vertical, diagonal, metal-centered, and oxygen-centered mesoscopic stripe patterns of localized holes (small polarons). This represents important inhomogeneous magneto-elastic coupling.