A scaling relation Nc or ρs ασdcΤc has been observed in the copper-oxide superconductors, where ρs is the superconducting condensate and the spectral weight is Nc=ρs/8, Tc is the critical temperature, and σdc is the normal-state dc conductivity close to Tc. This scaling relation is examined within the context of clean and dirty-limit BCS superconductors. It is shown that the scaling relation Nc ≃ 4.4σdcTc, which follows directly from the Ferrell-Glover-Tinkham sum rule, is the hallmark of a BCS system in the dirty-limit. 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 scales linearly with Tc. 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 pictures may be viewed as equivalent.
The optical conductivity ((sigma) 1) of twinned and untwinned single crystals of YBa2(Cu1-xNix)3O6.95 has been studied using infrared reflectance spectroscopy for x equals 0, 0.75 and 1.4% ('pure,' 'light' and 'heavily' doped). The optical properties have been calculated from a Kramers-Kronig analysis of the reflectance. Nickel acts as a point defect scatterer in the planes, but has only a small effect on Tc. (At the heaviest Ni doping, Tc is only suppressed by approximately equal to 4 K). In the pure, twinned samples for T very much less than Tc, there is a narrow, 'Drude'-like band at low frequency; the conductivity is observed to drop to a minimum of approximately equal to 1000 (Omega) -1 cm-1 at approximately equal to 500 cm-1 before gradually rising to join a temperature-independent midinfrared band. In the heavily- doped sample, there is a large amount of low-frequency residual conductivity; at 6 K some of the residual conductivity has been suppressed and a shoulder in (sigma) 1 is visible at approximately equal to 300 cm-1. In the lightly-doped sample, the approximately equal to 300 cm-1 shoulder is visible already at 12 K. However, in the same detwinned sample, the shoulder in (sigma) 1 is observed only for E (parallel) b, and is present in the normal state indicating that this feature is associated with the chains, and is not related to the superconductivity in these materials. The origin of this feature is discussed, and it is proposed that the shoulder at approximately equal to 300 cm-1 may be related to the pseudogap observed along the c axis in the oxygen-underdoped materials.
The combination of lowered dimensionality and electron-electron correlations are responsible for the unusual temperature and frequency dependence of the electrical conductivity of the new superconductors. We first review the electrodynamics of two systems, U2Ru2Si2 and Sr2RuO4 where conventional Fermi liquid ideas seem to work. Here transport is by free carriers with strongly renormalized masses. On the other hand the electrodynamics of the high Tc cuprates and the organic charge transfer salts is unconventional. The high Tcs show a Drude peak with an anomalous temperature and frequency dependent scattering rate for the in-plane conductivity, while normal to the planes they are almost insulating. In the organics, the transport currents are carried by a narrow collective mode coupled to phonons.
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