Small-polaron formation and optical absorption in Su-Schrieffer-Heeger and Holstein models

The conditions leading to small-polaron formation for a single charge carrier in the Su-Schrieffer-Heeger (SSH) model are compared with the Holstein model. From analytic perturbation theory and exact numerical diagonalization of small clusters different criteria are established, which however have a common physical origin: Polaron formation requires a sizable mass enhancement and a lattice deformation energy gain larger than the loss in the bare electron kinetic energy in both models. The optical absorption of the Su-Schrieffer-Heeger model in the polaronic regime is also shown to exhibit an additional feature not present in the Holstein model. This additional feature arises due to the bond nature of small polarons in the SSH model, and is determined by transitions from the ground state of the bonding character on a shortened bond to excited states of the antibonding character on the same shortened bond.