A phenomenological model comprehensively captures the defining features of the cuprate high-temperature superconductors.

A pivotal step toward understanding unconventional superconductors would be to decipher how superconductivity emerges from the unusual normal state. In the cuprates, traces of superconducting pairing appear above the macroscopic transition temperature T_c, yet extensive investigation has led to disparate conclusions. The main difficulty has been to separate superconducting contributions from complex normal-state behaviour. Here we avoid this problem by measuring nonlinear conductivity, an observable that is zero in the normal state. We uncover for several representative cuprates that the nonlinear conductivity vanishes exponentially above T_c, both with temperature and magnetic field, and exhibits temperature-scaling characterized by a universal scale Ξ₀. Attempts to model the response with standard Ginzburg-Landau theory are systematically unsuccessful. Instead, our findings are captured by a simple percolation model that also explains other properties of the cuprates. We thus resolve a long-standing conundrum by showing that the superconducting precursor in the cuprates is strongly affected by intrinsic inhomogeneity.

Microwave absorption measurements in magnetic fields from 0 up to 16 T were used to determine the temperature range of superconducting fluctuations above the superconducting critical temperature Tc in YBa2Cu3O7-$\delta${}. Measurements were performed on deeply underdoped, slightly underdoped, and overdoped single crystals. The temperature range of the superconducting fluctuations above Tc is determined by an experimental method which is free from arbitrary assumptions about subtracting the nonsuperconducting contributions to the total measured signal and/or theoretical models to extract the unknown parameters. The superconducting fluctuations are detected in the ab plane, and c-axis conductivity, by identifying the onset temperature T$'${}. Within the sensitivity of the method, this fluctuation regime is found only within a fairly narrow region above Tc. Its width increases from 7 K in the overdoped sample (Tc=89$\hskip0.3em${}K) to, at most, 23 K in the deeply underdoped sample (Tc=57$\hskip0.3em${}K), so that T$'${} falls well below the pseudogap temperature T*. Implications of these findings are discussed in the context of other experimental probes of superconducting fluctuations in the cuprates.

The microwave response of high quality niobium films in a perpendicular static magnetic field has been investigated. The complex frequency shift was measured up to the upper critical fields. The data have been analyzed by the effective conductivity model for the type-II superconductors in the mixed state. This model is found to yield consistent results for the coherence lengths in high-$\kappa$ superconducting samples, and can be used with high-temperature superconductors even at temperatures much below $T_c$. It is shown that for samples with high values of depinning frequency, one should measure both components of the complex frequency shift in order to determine the flow resistivity. The thick Nb film $\left(160\mathrm{nm}\right)$ has low resistivity at $10\mathrm{K}$, comparable to the best single crystals, and low $\kappa$ value. In contrast, the thinnest $\left(10\mathrm{nm}\right)$ film has $\kappa \approx 9.5$ and exhibits a high depinning frequency $(\approx 20\mathrm{GHz})$. The upper critical field determined from microwave measurements is related to the radius of nonoverlaping vortices, and appears to be larger than the one determined by the transition to the normal state.

Despite extraordinary scientific efforts over the past three decades, the cuprate high-temperature superconductors continue to pose formidable challenges. A pivotal problem, essential for understanding both the normal and superconducting states, is to clarify the nature of the superconducting pre-pairing above the bulk transition temperature T_c. Different experimental probes have given conflicting results, in part due to difficulties in discerning the superconducting response from the complex normal-state behavior. Moreover, it has proven challenging to separate common properties of the cuprates from compound-specific idiosyncrasies. Here we investigate the paraconductivity—the superconducting contribution to the direct-current (dc) conductivity—of the simple-tetragonal model cuprate material HgBa₂CuO_4+δ. We are able to separate the superconducting and normal-state responses by taking advantage of the Fermi-liquid nature of the normal state in underdoped HgBa₂CuO_4+δ; the robust and simple quadratic temperature-dependence of the normal-state resistivity enables us to extract the paraconductivity above the macroscopic T_c with great accuracy. We find that the paraconductivity exhibits unusual exponential temperature dependence, and that it can be quantitatively explained by a simple superconducting percolation model. Consequently, the emergence of superconductivity in this model system is dominated by the underlying intrinsic gap inhomogeneity. Motivated by these insights, we reanalyze published results for two other cuprates and find exponential behavior as well, with nearly the same characteristic temperature scale. The universal intrinsic gap inhomogeneity is not only essential for understanding the supercoducting precursor, but will also have to be taken into account in the analysis of other bulk measurements of the cuprates.