Two-fluid interpretation of the microwave conductivity ofYBa2Cu3

Abstract

The use of the two-fluid model for analyzing the microwave conductivity of YBa 2 Cu 3 O 7Ϫ␦ is critically appraised for s-wave and d-wave models and for weak and strong scattering, in the light of published results on single crystals, and of results here presented on high-quality epitaxial films and powders doped with Zn and Co. It is argued that the normal electrons in the best samples show nonlocal conductivity ͑Ͻl below 40 K͒, and that this provides a natural explanation of the low-temperature behavior of the measured surface impedance. If correct this model is firmly in favor of d-wave pairing. Evidence is shown that some 10% of electrons remain normal at Tϭ0 in good films and 50% or more in heavily doped powders, in states which may or may not be localized. This behavior is associated with a T 2 term in the temperature dependence of and is in accord with recent calculations of the effects of strong scattering impurities. It is argued that in the superconducting state transport between localized states is not necessarily associated with hopping conduction, because of the effects of Andreev reflection.

Low-energy quasiparticles in high- T c cuprates

“…Waldram et al also pointed out that non-local e ects might become important below 20 K, where the width of the conductivity peak is narrow and almost temperature-independent , leading to an e ective scattering rate that is not in¯uenced by the density of residual impurities [126]. However, the reduced narrowing observed by Hardy's group in going from yttria-stablized-zirconi a to BaZrO3 crucibles suggests that YBa2Cu3O7¡¯crystals are still in a regime where impurities play a role in the low-frequency scattering [40].…”

Electrical transport measurements in the superconducting state ofBi2Sr2CaCu2O8

“…2,16,17,18,33 For y = 2 there are closed-form expressions for the relaxation rate and normal-fluid fraction:…”

“…This has been a somewhat speculative endeavor in the past, with only limited experimental data available to support the assumption of a Lorentzian conductivity spectrum. 2,16,17,18 The two-fluid description of the conductivity we adopt here is based on a phenomenological conductivity spectrum σ 1 (ω) that has been carefully validated through detailed spectroscopic measurements on YBa 2 Cu 3 O 6+x . 10,19 Nevertheless, we take care to show that the qualitative form of the temperature-dependent relaxation rate inferred from this analysis is quite insensitive to the assumed form of the conductivity spectrum.…”

Order-parameter holes and theory of microwave conductivity inYBa2Cu3O<

“…Measurements on yttria-stabilized zirconia crucible-grown, nominally pure, YBCO crystals at low frequencies Ω of order a few GHz showed an apparently linear temperature dependence, σ ∼ T for temperatures T sufficiently far below a large peak at 30-40K. [4,6] Theories of the dynamical conductivity in the d-wave state [7,8] have been successful in explaining roughly the size and position, as well as the frequency and disorder dependence of the peak. However, at low temperatures and small microwave frequencies, where transport is dominated by elastic scattering and the theory should be simplest, the theoretical prediction is σ ∼ T 2 , not T .…”