Effect of Extended Saddle Point Singularities in Cuprates and Evidences

First-principles calculations and angle-resolved photoemission spectroscopy measurements showed extended saddle point singularities in the electron structures of some cuprates such as YBa$_{\mathrm{2}}$Cu$_{\mathrm{3}}$O$_{\mathrm{7}}$ (YBCO). The extended saddle point singularities in the electronic structures of the materials can lead to anomalous physical properties. In this work, a new methodology is implemented by integrating first-principles calculations of electronic structures of the materials into the theory of many-body physics for superconductivity. The aim is to seek a unified methodology to calculate the electronic and superconducting properties of the materials. It is demonstrated from first-principles that the extended saddle point singularities in the materials such as YBCO strongly correlate to the anomalous isotope effect in the superconductors.