Thermodynamic evidence for a density-of-states peak near the Fermi level in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{y}}$

Thermodynamic properties such as the specific-heat discontinuity at the transition temperature (${\mathit{T}}_{\mathit{c}}$), ΔC/${\mathit{T}}_{\mathit{c}}$, and the zero-temperature critical field, ${\mathit{H}}_{\mathit{c}}$(0), of oxygen-deficient ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{y}}$ are analyzed to show that, within the framework of the BCS formalism, the density of states (DOS) at the Fermi level is peaked at y=0. The energy dependence of the DOS is considered for several models and found to be consistent with the Fermi level lying close to a two-dimensional van Hove singularity.