Emergence of superconductivity in the cuprates via a universal percolation process

A pivotal step toward understanding unconventional superconductors would be to decipher how superconductivity emerges from the unusual normal state upon cooling. 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 the separation of superconducting contributions from complex normal state behaviour. Here we avoid this problem by measuring the 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 nearly universal scale $T_0$. Attempts to model the response with the frequently evoked Ginzburg-Landau theory are unsuccessful. Instead, our findings are captured by a simple percolation model that can also explain other properties of the cuprates. We thus resolve a long-standing conundrum by showing that the emergence of superconductivity in the cuprates is dominated by their inherent inhomogeneity

Percolative nature of the dc paraconductivity in the cuprate superconductors

We present an investigation of the planar direct-current (dc) paraconductivity of the model cuprate material HgBa$_2$CuO$_{4+\delta}$ in the underdoped part of the phase diagram. The simple quadratic temperature-dependence of the Fermi-liquid normal-state resistivity enables us to extract the paraconductivity above the macroscopic $T_c$ with great accuracy. The paraconductivity exhibits unusual exponential temperature dependence, with a characteristic temperature scale that is distinct from $T_c$. In the entire temperature range where it is discernable, the paraconductivity is quantitatively explained by a simple superconducting percolation model, which implies that underlying gap disorder dominates the emergence of superconductivity

Demonstrating the model nature of the high-temperature superconductor HgBa2_2CuO4+Δ_{4+\Delta}

The compound HgBa$_2$CuO$_{4+\Delta}$ (Hg1201) exhibits a simple tetragonal crystal structure and the highest superconducting transition temperature (T$_c$) among all single Cu-O layer cuprates, with T$_c$ = 97 K (onset) at optimal doping. Due to a lack of sizable single crystals, experimental work on this very attractive system has been significantly limited. Thanks to a recent breakthrough in crystal growth, such crystals have now become available. Here, we demonstrate that it is possible to identify suitable heat treatment conditions to systematically and uniformly tune the hole concentration of Hg1201 crystals over a wide range, from very underdoped (T$_c$ = 47 K, hole concentration p ~ 0.08) to overdoped (T$_c$ = 64 K, p ~ 0.22). We then present quantitative magnetic susceptibility and DC charge transport results that reveal the very high-quality nature of the studied crystals. Using XPS on cleaved samples, we furthermore demonstrate that it is possible to obtain large surfaces of good quality. These characterization measurements demonstrate that Hg1201 should be viewed as a model high-temperature superconductor, and they provide the foundation for extensive future experimental work.Comment: 15 pages, 6 Figure

Two-component uniform spin susceptibility in superconducting HgBa2_{2}CuO4+δ_{4+\delta} single crystals determined with 63^{63}Cu and 199^{199}Hg NMR

$^{63}$Cu and $^{199}$Hg NMR shifts for an optimally and underdoped HgBa$_{2}$CuO$_{4+\delta}$ single crystal are reported, and the temperature dependence dictates a two-component description of the uniform spin susceptibility. The first component, associated with the pseudogap phenomenon in the NMR shifts, decreases already at room temperature and continues to drop as the temperature is lowered, without a drastic change at the transition temperature into the superconducting state. The second component is temperature independent above the superconducting transition temperature and vanishes rapidly below it. It increases with doping and is a substantial part of the total spin susceptibility measured at both nuclei