Correlation between crystal structure and resistivity of high-temperature superconducting cuprates

Abstract

The experimental resistivity of high temperature superconducting (HTSC) cuprates at about Tc has been determined by many authors. For large devices the in-CuO2-plane resistivity has a range of (~ 0.5 < ρ(exp) < ~15) • 10-6 Ωm. Above Tc all HTSC materials behave like a classical device and the resistance depends on cross section and length of the device. Assuming a superconducting unit volume and a mode structure, which are given by the doping pattern through-out the whole crystal, the experimental resistivity values have been plotted versus ~ LR/Nmode. It shows a strong linear correlation in the form ρ(exp) = m3 • (LR/Nmode) • (n4/n3) with a slope of m3 = (13.39 ± 0.79) • 103 Ω. LR is an effective resistivity length, Nmode is the number of CuO2 planes per unit cell, n3 is the number of Cu3+ -ions per chemical formula and n4 is the number of different shifted stacking sequences per unit cell. The value for m3 is very close to the fundamental resistance of a single-mode ballistic conductor Rsm = h/2e2 ≈12,906 Ω, which appears when size quantization plays a dominant role.