Effect of site-diagonal disorder on the polaronic crossover

The effect of the site diagonal binary-alloy-type disorder on the polaronic crossover has been studied for a 1d Holstein model. A variational method is followed to obtain an effective polaronic Hamiltonian. The site diagonal disorder is then treated with a real space renormalization group method. We find that the polaron shrinks in its size and the large-to-small polaron crossover occurs at a lower value of electron-phonon (e-ph) coupling with increasing disorder potential or concentration.