SCALING IN HIGH-TEMPERATURE SUPERCONDUCTORS

A Hartree approximation is used to study the interplay of two kinds of scaling which arise in high-temperature superconductors, namely criti cal-point scaling and that due to the confinement of electron pairs to their lowest Landau level in the presence of an applied magnetic fiel d. In the neighborhood of the zero-field critical point, thermodynamic functions scale with the scaling variable [T - T(c2)(B)]/B1/2nu, whic h differs from the variable [T - T(c)(0)]/B1/2nu suggested by the Gaus sian approximation. Lowest-Landau-level (LLL) scaling occurs in a regi on of high field surrounding the upper critical-field line but not in the vicinity of the zero-field transition. For YBa2Cu3O7-delta in part icular, a field of at least 10 T is needed to observe LLL scaling. The se results are consistent with a range of recent experimental measurem ents of the magnetization, transport properties, and, especially, the specific heat of high-T(c) materials.