Scaling of the superfluid density in high-temperature superconductors

TL;DR

This paper investigates the scaling relation between superfluid density, conductivity, and critical temperature in high-temperature superconductors, suggesting they operate in the dirty-limit BCS regime and exploring implications for their pairing mechanism.

Contribution

It demonstrates that the observed scaling relation indicates high-Tc cuprates are in the dirty-limit BCS regime, linking superfluid density to normal-state conductivity and T_c, and discusses implications for their superconducting nature.

Findings

Scaling relation  ho_s \u2248 35  \sigma_{dc} T_c observed in cuprates

Cuprates likely operate in the dirty-limit BCS regime

Dirty-limit behavior relates to the energy scale of condensate formation

Abstract

A scaling relation \rho_s \simeq 35\sigma_{dc}T_c has been observed in the copper-oxide superconductors, where \rho_s is the strength of the superconducting condensate, T_c is the critical temperature, and \sigma_{dc} is the normal-state dc conductivity close to T_c. This scaling relation is examined within the context of a clean and dirty-limit BCS superconductor. These limits are well established for an isotropic BCS gap 2\Delta and a normal-state scattering rate 1/\tau; in the clean limit 1/\tau \ll 2\Delta, and in the dirty limit 1/\tau > 2\Delta. The dirty limit may also be defined operationally as the regime where \rho_s varies with 1/\tau. It is shown that the scaling relation \rho_s \propto \sigma_{dc}T_c is the hallmark of a BCS system in the dirty-limit. While the gap in the copper-oxide superconductors is considered to be d-wave with nodes and a gap maximum \Delta_0, if 1/\tau > 2\Delta_0 then the dirty-limit case is preserved. The scaling relation implies that the copper-oxide superconductors are likely to be in the dirty limit, and that as a result the energy scale associated with the formation of the condensate is scaling linearly with T_c. The a-b planes and the c axis also follow the same scaling relation. It is observed that the scaling behavior for the dirty limit and the Josephson effect (assuming a BCS formalism) are essentially identical, suggesting that in some regime these two effects may be viewed as equivalent. This raises the possibility that electronic inhomogeneities in the copper-oxygen planes may play an important role in the nature of the superconductivity in the copper-oxide materials.