Effect of Uniaxial Pressure on the Isotope Effect on the Spectrum of Hamiltonians with Electron–Phonon Coupling

We have studied the effect of a change in the equilibrium nearest neighbour distances on the dynamics of charge and ions on a three-site cluster, identified with an O–Cu–O cluster present in high temperature superconductors. We consider a model Hamiltonian that contains an electronic part represented by a single band Hubbard model with onsite electronic correlations and a phononic part consisting of non-interacting Raman and infrared active phonons. The electron–phonon coupling is introduced through the change in interatomic distances generated by Coulomb repulsion between charges at neighbouring sites. For intermediate and strong values of the electron–phonon coupling, this model generates correlated electron–ion motion, i.e., polaron formation. In order to simulate the effect of change in the equilibrium nearest neighbour distances, we assume that the main effect such a change is a variation of the intersite electron hopping probability, t. We, therefore, studied the excitation spectrum of this model and the local lattice distortion in the Cu–O bond length as a function of t. We also studied the effect of a change in t in the polaron tunnelling energy when we use different oxygen isotopic masses, i.e., O¹⁶ and O¹⁸. We find that as function of t, the isotopic shift does not show a monotonic behaviour, as it does as a function of the electron–phonon coupling constant. It exhibits a minimum for values of t for which the electron–phonon coupling generates local lattice distortions with magnitudes similar to those observed experimentally in high-temperature superconductors. This observation could be related with the observed maximum on T _c as a function of the microstrain of the Cu–O bonds (Sanna et al. in Int. J. Mod. Phys. B 14(29–31), 2000; Bianconi et al. in J. Phys.: Condens. Matter 12:10655, 2000; Agrestini et al. in J. Phys. A: Math. Gen. 36:9133, 2003).