Physics – Condensed Matter – Superconductivity
Scientific paper
2004-10-27
Phys. Rev. B 72, 134517 (2005) (8 pages)
Physics
Condensed Matter
Superconductivity
8 pages with 5 figures and 1 table
Scientific paper
10.1103/PhysRevB.72.134517
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.
Dordevic S. V.
Homes Christopher C.
Strongin M.
Valla Tomas
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