Saddle-point pairing: An electronic mechanism for superconductivity

It is shown that the interactions in a strongly correlated quasi-two-dimensional electron gas with the Fermi level lying at a saddle point (Van Hove singularity) in ${\mathrm{\varepsilon }}_{\mathit{k}}$ can give rise to superconductivity by exchange of excitations with a characteristic low electronic energy scale ${\mathit{E}}^{\mathrm{*}}$. Application to cuprate superconductors shows that this mechanism along with a conventional electron-phonon interaction can explain the high ${\mathit{T}}_{\mathit{c}}$’s and the anomalous behavior of the isotope shift as a function of doping.