Extended Electron Saddle Point Singularities and the Anomalous Isotope Effect in Zr, Nb₃Sn, and YBa₂Cu₃O₇

Anomalously small isotope effect in some high and low T_c superconductors such as Zr, Nb₃Sn, and YBa₂Cu₃O₇ (YBCO) created a great challenge for understanding. It has been shown by experiments and first-principles quantum calculations that there exist extended saddle point singularities around the Fermi levels in the electronic structures of these materials. In this work, a method is implemented by integrating first-principles quantum computations of electronic structures of the materials into the microscopic quantum theory of many-body physics for superconductivity. The aim is to seek a unified methodology based on first-principles microscopic quantum theory to calculate the electronic and superconducting properties of these materials. It is demonstrated from first-principles that the extended saddle point singularities around the Fermi levels in Zr, Nb₃Sn, and YBCO strongly correlate to the anomalous isotope effect in these superconductors.