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.

By means of nuclear spin-lattice relaxation rate T1-1, we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system NiCl2-4SC(NH2)2 and the spin-ladder system (C5H12N)2CuBr4. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, T1-1 exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for T1-1, compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.

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.

An approach to microwave measurements is used in order to determine both, the in-plane and out-of-plane conductivity of the high-$T_c$ superconductor ${\text{HgBa}}_2{\text{CuO}}_{4+\delta }$ near optimal doping. Unlike the $ab$-plane conductivity, the $c$-axis conductivity is highly sensitive to superconducting fluctuations. From a single $c$-axis data set, we can clearly discern the opening of the pseudogap at $T^{\ast }=185\left(15\right)\text{K}$, the appearance of the superconducting fluctuations at a much lower temperature $T^{\prime }=105\left(2\right)\text{K}$, and the full transition to the superconducting state at the critical temperature $T_c=94.3\text{K}$. Thus, with the present high sensitivity, we establish that the extent of the superconducting fluctuations is only about $10\text{K}$ above $T_c$.

Nuclear magnetic resonance study of the high magnetic field $\left(H\right)$ part of the Bose-Einstein condensed (BEC) phase of the quasi-one-dimensional (quasi-1D) antiferromagnetic quantum spin-chain compound ${\mathrm{NiCl}}_2\text{−}4\mathrm{SC}{\left({\mathrm{NH}}_2\right)}_2$ was performed. We precisely determined the phase boundary, $T_{\mathrm{c}}\left(H\right)$, down to 40 mK; the critical boson density, $n_{\mathrm{c}}\left(T_{\mathrm{c}}\right)$; and the absolute value of the BEC order parameter $S_{\perp }$ at very low temperature $(T=0.12\mathrm{K})$. All results are accurately reproduced by numerical quantum Monte Carlo simulations of a realistic three-dimensional (3D) model Hamiltonian. Approximate analytical predictions based on the 1D Tomonaga-Luttinger liquid description are found to be precise for $T_{\mathrm{c}}\left(H\right)$, but less so for $S_{\perp }\left(H\right)$, which is more sensitive to the strength of 3D couplings, in particular close to the critical field. A mean-field treatment, based on the Hartree-Fock-Popov description, is found to be valid only up to $n_{\mathrm{c}}\cong 4\%$ $(T<0.3$ K), while for higher $n_{\mathrm{c}}$ boson interactions appear to modify the density of states.