| dc.description.abstract | In this chapter, we have presented a theory for muon-spin-rotation (?SR) spectra in anisotropic, layered superconductors, incorporating thermal effects in both the solid and liquid phases. We now discuss, in some detail, the consequences of our results.
While our theory provides, in principle, a self-consistent description of the role of thermal effects in producing linewidth narrowing-similar to what is observed in experiments on BSCCO-the linewidths we obtain using ? values of 1500 Å are still too large compared to experimental data. However, our results represent a considerable improvement over those obtained using the standard zero-temperature description of the solid phase.
Our data reveal an interesting feature from the analysis of the relations for ?B²?: increasing correlations in the layer plane suppress the value of this moment, whereas increasing correlations along the c-axis direction enhance it. This feature may be observable in experiments.
Although our theory reproduces most qualitative features of the experimental data, a significant discrepancy remains between the calculated and observed linewidths. It is important to note that several assumptions are made during experimental analysis before linewidths are extracted-such as corrections for instrumental resolution and statistical fluctuations. Additionally, fitting functions (e.g., truncated back-to-back exponentials for the field distribution function [81]) are commonly used to deconvolute the data. The sensitivity of the resulting distributions and moments to the data treatment method remains questionable.
For instance, Harshman et al. [81] report remarkably symmetric lineshapes-even deep into the presumed solid phase-with little evidence of the expected Van Hove singularities in n(B)n(B)n(B). The reason for this at very low temperatures is unclear.
Recent data from Lee et al. [21] present another puzzle: the temperature dependence of the second moment of the field distribution (at low fields ~0.4 kG) appears to show evidence of two-fluid behavior, contrary to Harshman et al.'s measurements at slightly higher fields. Unlike Harshman et al., Lee et al.'s data for n(B)n(B)n(B) show noticeable asymmetry in the solid phase. Moreover, the flux-lattice melting transition is clearly visible in their work through abrupt changes in both the second moment of the field distribution and an asymmetry parameter (defined as the ratio of the third to second moments of n(B)n(B)n(B)). Harshman et al. observe no such abrupt change in ??B²? as temperature varies.
Given these discrepancies between different experiments on the same system, further investigation is needed to clarify the behavior of n(B)n(B)n(B) in BSCCO.
We now consider other possible reasons for the discrepancy between our results and experimental data. First, using slightly higher values of ? could reduce the discrepancy. Although such values would be inconsistent with melting temperatures around 20 K in the high-field limit indicated by our phase diagram, it might be possible to correct for this using a more accurate liquid-state description. As argued in Chapter 1, our freezing temperatures should be considered lower bounds for the experimental system, given the approximations in our liquid-state methods.
Second, the overestimation of equilibrium ??B²? values may arise because the density functional description does not account for all classes of fluctuations in the solid phase. One such class involves Gaussian ansatz-based density distributions-moving these Gaussians around their equilibrium positions introduces additional fluctuations that further renormalize ??B²?. These excitations are similar to phonons and have been discussed in density functional contexts [87].
Third, we assume the flux-lattice can be treated classically-i.e., the Debye temperature (which sets the scale below which quantum effects become significant) lies well below the equilibrium melting temperature. This assumption has been challenged by Bulaevskii and collaborators [84], who argue that quantum effects are non-negligible except very close to the superconducting transition temperature TcT_cTc. Their argument is based on the idea that the characteristic energy scale for quantum effects is set by the gap and is therefore ~kBTck_B T_ckBTc. While much remains to be understood about quantum effects in the mixed phase, the success of the density functional approach in describing flux-lattice melting-assuming a classical liquid-state description-serves as a counterexample to the claim that quantum effects must be included in any theory of the mixed phase. As emphasized earlier, our theory underestimates the freezing curve, and quantum effects would likely depress it further.
To conclude, we have demonstrated that thermal effects play a significant role in determining linewidth narrowing in ?SR spectra within the mixed phase of strongly anisotropic high-TcT_cTc cuprates. In the solid phase, the density functional description of the time-averaged density distribution offers a unique, non-perturbative way to assess thermal broadening. Our discussion of ?SR spectra in the liquid phase represents, to the best of our knowledge, the first attempt to calculate linewidths in this phase beyond the simplest assumption of uncorrelated lines or vortices. | |
