Percolative aspects of cuprate superconductivity

One of the central problems in the physics of the cuprate high-temperature superconductors is understanding the superconducting emergence regime above the macroscopic critical temperature Tc. The emergence regime provides crucial information about both the normal and superconducting states and has long been the subject of controversy. Experimentally, it is difficult to separate the nascent superconducting response from the complex normal-state behavior, with different experimental probes leading to disparate conclusions. We present a systematic investigation of the emergence of superconductivity in the cuprates using an unconventional probe: nonlinear conductivity. This probe eliminates background subtraction problems because the signal vanishes in the normal state. Through experiments on several cuprate families and as a function of doping, we show that the emergence regime is universally confined to a narrow temperature range, but incompatible with standard Ginzburg-Landau theory. Instead, a single characteristic temperature scale T0 controls superconductivity emergence. To explain the experiments, we introduce a simple superconducting percolation model based on local gap disorder, which provides a quantitative description of our measurements and explains several puzzling prior results. The success of the percolation model shows that intrinsic disorder plays an important role in cuprate superconductivity, enabling us to create an overarching picture of the charge-carrier behavior in the cuprates.