The unconventional temperature variation of the static susceptibility $\chi \mathrm{}\left(T\right)\mathrm{}$ that has been discovered in various copper oxide superconductors is explained in terms of a model density of states that has a step shape at an energy threshold $E_0$ along with a logarithmic Van Hove singularity at the same $E_0$. Calculations of $\chi \mathrm{}\left(T\right)\mathrm{}$ and the Knight shift above the superconducting transition temperature $T_c$ yield good fits to the YBCO, BSCCO, and LSCO data by adjusting only the Fermi energy $\mu$ in correspondence to the oxygen or Sr content, respectively. When $\mu$ is right on or slightly below the Van Hove singularity, an upturn in $\chi$ occurs as the temperature $T$ is lowered. By contrast, when $\mu$ is slightly above the threshold energy $E_0$, a downturn in $\chi$ is achieved as $T$ is lowered. A correlation of these phenomena with experimental data provides insight into the proximity of the Van Hove singularity to $\mu$ in several cuprate superconductors. The YBCO and TBCO cuprates with the higher $T_c$ values exhibit a nearly constant susceptibility that suggests a Fermi energy well removed from the Van Hove singularity. The sensitivity of $T_c$ as well as the susceptibility to chemical changes may provide tests of electronic mechanisms of electron pairing as well as the BCS theory.

• Received 19 August 1994

DOI:https://doi.org/10.1103/PhysRevB.51.15393