Microscopic theory of atomic and electronic stretched exponential relaxation in high temperature superconductors

Measured dimensionless room-temperature conductivity relaxation stretching fractions β in YBCO are in excellent agreement with theoretical predictions, which in 1995 identified two magic fractions, β=3/5 and β=3/7. Thus, relaxation studies provide an absolute measure of “ideality” in these complex materials, independent not only of composition x but even of crystal structure. The relaxation stretching fractions β associated with T_c itself, reported in 2000, are also explained by the magic fraction β=3/5 predicted by microscopic theory. One can infer that the interactions responsible for high-temperature superconductivity are short range, non-magnetic, and primarily associated with resonant trapping centers in semiconductive layers.