Visualizing pair formation on the atomic scale in the high-T_c superconductor Bi₂Sr₂CaCu₂O_8+δ

Pairing of electrons in conventional superconductors occurs at the superconducting transition temperature T_c, creating an energy gap Δ in the electronic density of states (DOS). In the high-T_c superconductors, a partial gap in the DOS exists for a range of temperatures above T_c (ref. 2). A key question is whether the gap in the DOS above T_c is associated with pairing, and what determines the temperature at which incoherent pairs form. Here we report the first spatially resolved measurements of gap formation in a high-T_c superconductor, measured on Bi₂Sr₂CaCu₂O_8+δ samples with different T_c values (hole concentration of 0.12 to 0.22) using scanning tunnelling microscopy. Over a wide range of doping from 0.16 to 0.22 we find that pairing gaps nucleate in nanoscale regions above T_c. These regions proliferate as the temperature is lowered, resulting in a spatial distribution of gap sizes in the superconducting state. Despite the inhomogeneity, we find that every pairing gap develops locally at a temperature T_p, following the relation 2Δ/k_BT_p = 7.9 ± 0.5. At very low doping (≤0.14), systematic changes in the DOS indicate the presence of another phenomenon, which is unrelated and perhaps competes with electron pairing. Our observation of nanometre-sized pairing regions provides the missing microscopic basis for understanding recent reports of fluctuating superconducting response above T_c in hole-doped high-T_c copper oxide superconductors.