Large low-symmetry polarons of the high-T-c copper oxides: Formation, mobility and ordering

A microscopic model of the evolution from antiferromagnetic insulator to superconductor on oxidation of the parent-phase (CuO2)(2-) sheets of a cuprate superconductor starts with the assumption that strong electron-lattice interactions are dominant and give a heterogeneous electronic distribution. Introduction of pseudo-Jahn-Teller vibronic coupling associated with the delta holes in the (CuO2)((2-delta)-) sheets is shown to stabilize, below a critical temperature T-p approximate to 850 K, large non-adiabatic polarons containing 5 to 7 copper centers; cooperative low-symmetry in-plane vibrations also stabilize an elastic attractive force between polarons that can overcome the longer-range Coulomb repulsion between polarons. Utilizing established parameters for isolated CuO6 complexes gives a calculated polaron size of 5 to 7 copper centers, which compares with a measured mean size of 5.3 copper centers in underdoped samples 0 < delta < 0.10. A large polaron is shown to move by a piece-wise tunneling of a fraction of itself across a peripheral Cu-O vibronic bond rather than by an activated hopping. This type of motion, which is not described by conventional transport theories, gives a linear increase of the resistivity with temperature above a temperature T-p due to scattering of the polaron at its own border, which separates regions inside and outside the polaron of slightly different mean Cu-O bond length. At lower temperatures, the polaron mobility becomes activated, but at higher concentrations this change is obscured because the elastic interpolaron attractive force causes the polarons to condense into a ''polaron liquid,'' and below some critical temperature T-d greater than or equal to T-c the polarons undergo long-range ordering into one-dimensional [110] polaronic stripes separated by stripes of the parent phase, which support antiferromagnetic spin fluctuations. The zig-zag polaron stripes consist of polaron pairs oriented alternately along [100] and [010] axes of a CuO2 sheet. Formation of the ordered superstructure permits conduction of hole pairs without scattering from lattice vibrations provided there is also coupling in the third dimension between CuO2 sheets. The vibronic coupling introduces an anisotropic dispersion curve and superconductive gap for the states within the polarons, which lie within the energy gap between residual Hubbard-band states of the parent phase. The magnitude of the superconductive gap is determined by the elastic forces responsible for ordering the superstructure rather than by the energy of coupling of superconductive pairs.