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

TL;DR

This paper investigates how polarons in the Hubbard-Holstein model can lead to d-wave superconductivity, especially during the large to small polaron crossover, with small transition temperatures and no s-wave pairing under repulsive interactions.

Contribution

It introduces a residual kinematic interaction as a pairing mechanism for polarons and analyzes the conditions for d-wave superconductivity in the model.

Findings

Superconducting instability occurs in the d-wave channel.

Maximum transition temperature is in the large to small polaron crossover region.

No s-wave superconductivity when on-site interaction is repulsive.

Abstract

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.