Electron – lattice coupling in HTSC cuprates: Evidence for polaron formation from unconventional isotope and strain effects

Motivated by recent Andreev reflection experiments we use a two- component scenario to study lattice effects on the superconducting transition temperature T$_{c}$, the isotope exponent and strain effects in high temperature superconducting copper oxides. We find that the polaronic renormalization of the single particle energies substantially enhances T$_{c}$, can explain the strain induced enhancement of T$_{c}$ and yields the unconventional isotope effect on the London penetration depth $\lambda _{L}$. The lattice distortion which causes these effects is identified as the Q$_{2}$-type Jahn-Teller mode.