Scaling in high-temperature superconductors

TL;DR

This paper investigates the scaling behaviors in high-temperature superconductors near critical points, highlighting differences from gaussian approximations and the conditions for observing Landau-level scaling, with implications for experimental measurements.

Contribution

It introduces a Hartree approximation analysis revealing distinct scaling variables and conditions for Landau-level scaling in high-$T_c$ superconductors, refining previous theoretical models.

Findings

Thermodynamic functions scale with $(T-T_{c2}(B))/B^{1/2 u}$ near zero-field critical point.

LLL scaling occurs only at high magnetic fields, not near zero-field transition.

At least 10 T magnetic field is required to observe LLL scaling in YBaCuO.

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 neighbourhood of the zero-field critical point, thermodynamic functions scale with the scaling variable $(T-T_{c2}(B))/B^{1/2\nu}$, which differs from the variable $(T - T_c(0))/B^{1/2\nu}$ 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 YBaCuO 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-$T_c$ materials.