Scaling in high-temperature superconductors

Abstract

A Hartree approximation is used to study the interplay of two kinds of scaling which arise in high-temperature superconductors, namely critical-point scaling and that due to the confinement of electron pairs to their lowest Landau level in the presence of an applied magnetic field. In the neighborhood of the zero-field critical point, thermodynamic functions scale with the scaling variable [T-Tc2(B)]/B1/2ν, which differs from the variable [T-Tc(0)]/B1/2ν suggested by the Gaussian approximation. Lowest-Landau-level (LLL) scaling occurs in a region of high field surrounding the upper critical-field line but not in the vicinity of the zero-field transition. For YBa2Cu3O7−δ in particular, a field of at least 10 T is needed to observe LLL scaling. These results are consistent with a range of recent experimental measurements of the magnetization, transport properties, and, especially, the specific heat of high-Tc materials.