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Pairing of electrons in conventional superconductors occurs at thesuperconducting transition temperature Tc, creating an energy gap D in theelectronic density of states (DOS). In the high-Tc superconductors, a partialgap in the DOS exists for a range of temperatures above Tc. A key question iswhether the gap in the DOS above Tc is associated with pairing, and whatdetermines the temperature at which incoherent pairs form. Here we report thefirst spatially resolved measurements of gap formation in a high-Tcsuperconductor, measured on Bi2Sr2CaCu2O8+d samples with different Tc values(hole concentration of 0.12 to 0.22) using scanning tunnelling microscopy. Overa wide range of doping from 0.16 to 0.22 we find that pairing gaps nucleate innanoscale regions above Tc. These regions proliferate as the temperature islowered, resulting in a spatial distribution of gap sizes in thesuperconducting state. Despite the inhomogeneity, we find that every pairinggap develops locally at a temperature Tp, following the relation 2D/kBTp = 8.At very low doping (<0.14), systematic changes in the DOS indicate the presenceof another phenomenon, which is unrelated and perhaps competes with electronpairing. Our observation of nanometre-sized pairing regions provides themissing microscopic basis for understanding recent reports of fluctuatingsuperconducting response above Tc in hole-doped high-Tc copper oxidesuperconductors.

Visualizing pair formation on the atomic scale in the high-Tc superconductor Bi2Sr2CaCu2O8+d