Anomalous isotope effect and Van Hove singularity in superconducting Cu oxides

Abstract

High-${\mathit{T}}_{\mathit{c}}$ Cu oxides such as ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ and the Bi-Sr-Ca-Cu-O systems are characterized by a near-zero oxygen-isotope effect. Recent results by Crawford et al. show, however, that the isotope effect in the ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_4$ system depends strongly on the doping level (x) and can significantly exceed the BCS limit. Within the framework of the BCS phonon-mediated pairing, a logarithmic (2D) Van Hove singularity in the density of states can provide a basis for understanding these anomalous isotope effects and possibly the origin of high-temperature superconductivity.