Coexistence of charges trapped in local lattice distortions and free carriers in cuprates

The interplay of strong local electron-lattice and electron-electron intera ction is analyzed in the two-dimensional Hubbard-Holstein model using an ef fective single band Hamiltonian. The effect of the strain field acting on t he CuO2 plane and the local cooperative pseudo Jahn Teller vibronic electro n-lattice coupling appropriate to cuprate superconductors at optimum doping ji.e.; at doping larger than 1/8) are included via the effective next near neighbor electronic hopping integral t ' (determined by the strain field) close to the local vibronic frequency omega (o) (involved in the pseudo Jah n Teller electron lattice coupling). The system shows a characteristic feat ure of the physics of complex systems, the competition and fluctuation betw een two states: 1) a first phase of charges self trapped in domains with lo cal lattice distortions (a generalisation to a many polaron system of the i dea of single intermediate polaron) and 2) a second phase of free carriers.