A universal scaling relation in high-temperature superconductors

Abstract

Since the discovery of superconductivity at elevated temperatures in the copper oxide materials there has been a considerable effort to find universal trends and correlations amongst physical quantities, as a clue to the origin of the superconductivity. One of the earliest patterns that emerged was the linear scaling of the superfluid density (rho(s)) with the superconducting transition temperature (T(c)), which marks the onset of phase coherence. This is referred to as the Uemura relation, and it works reasonably well for the underdoped materials. It does not, however, describe optimally doped (where T(c) is a maximum) or overdoped materials. Similarly, an attempt to scale the superfluid density with the d.c. conductivity (sigma(dc)) was only partially successful. Here we report a simple scaling relation (rho(s) proportional, variant sigma(dc)T(c), with sigma(dc) measured at approximately T(c)) that holds for all tested high-T(c) materials. It holds regardless of doping level, nature of dopant (electrons versus holes), crystal structure and type of disorder, and direction (parallel or perpendicular to the copper-oxygen planes).

An inhomogeneous Josephson phase in thin-film and high-Tc superconductors

“…Here we review and strengthen the arguments of Ref. [1] and discuss their relevance to the intriguing n s -T c correlations [5,6,7,8].…”

Tcfor heavy fermion superconductors linked with other physical properties at zero and applied pressure

“…1 appears relatively robust, as evidenced by the addition of quite recent data. The classification of HF materials is clearly quite different from the high-T c regularity plus Nb and Pb discussed by Homes et al [3] and also by Zaanen [4]. However, the Uncertainty Principle relaxation time τ UP is found to be of the same order of magnitude as that extracted from measured dc conductivity data plus effective masses at atmospheric pressure, namely τ (T c ).…”

“…In the same context, we have used the superconducting penetration depth λ 0 in Table 1 to estimate the superfluid density ρ s as λ −2 0 . Then, following Homes et al [3], if we construct ρ s /T c σ(T c ), then for all but one of the HF materials for which data is recorded in Table 1, this ratio is at least a factor of 7 greater than for high-T c materials, and with a huge scatter, confirming the above conclusion that HF materials are in a quite different category from high-T c materials plus the elemental BCS superconductors Nb and Pb.…”

“…(4) using experimental values for ρ(T c ), n n and m * . For comparison, we have also recorded the 'Uncertainty Principle' (UP) estimate τ UP given by Zaanen [4], following the study of Homes et al [3]:…”

“…Motivated by the study of Homes et al [3] on high-T c materials (plus elemental metals Nb and Pb with relatively high T c values for such superconductors) and of Zaanen [4], it is useful in connection with Table 1 to define a relaxation time τ (T c ) through [5] …”