Competing length scales in anharmonic lattices: Domains, stripes, and discommensurations

A two-dimensional anharmonic electron-lattice interaction model with higher-order density-density multiphonon interactions is solved exactly for arbitrary reciprocal-lattice vector q in the ionic limit as a model of a transition-metal oxide. Combining the harmonic and higher-order electron-phonon interaction terms into an effective coupling yields a strong q dependence of this coupling which changes sign when an on-site double-well potential occurs. Depending on the depth of this double-well potential various mesoscale structural and polarization patterns are found: stripes and domains, as well as incommensurate structural modulations. The results are related to experimental data for high-temperature superconductors, colossal magnetoresistance, and ferroelectric transition-metal perovskites, which probe local structural effects.