Polaron cross-overs and d-wave superconductivity in Hubbard-Holstein model

We present a theoretical study of superconductivity of polarons in the Hubbard-Holstein model. A residual kinematic interaction proportional to the square of the polaron hopping energy between polarons and phonons provides a pairing field for the polarons. We find that superconducting instability in the d-wave channel is possible with small transition temperatures which is maximum in the large to small polaron cross-over region. An s-wave instability is found to be not possible when the effective on-site interaction between polarons is repulsive.