Polaronic superconductivity in the absence of electron-hole symmetry

A major drawback of theories of superconductivity based on small polarons has been that the effective mass of the carriers becomes extremely large in the parameter regime where the effective interaction is attractive. An implicit assumption in these theories has been the existence of electron-hole symmetry. We consider here the Holstein model for small polarons and show that inclusion of electron-hole symmetry-breaking perturbations leads to a pairing mechanism that circumvents the above-mentioned difficulty. Such perturbations arise from a dependence of coupling constant and vibrational frequency on the density of carriers, as well as from anharmonicity in the vibrational potential. The possibility of using such a polaronic model arising from purely electron-phonon interactions to describe superconductivity in high-${\mathit{T}}_{\mathit{c}}$ oxides is considered. It is concluded that experimental evidence disfavors it, while it favors an electron-hole asymmetric small-polaron model arising from excitations with energies of electronic scale together with a small admixture of electron-phonon effects.