Imaging the energy gap modulations of the cuprate pair-density-wave state

The defining characteristic(1,2) of Cooper pairs with finite centre-of-mass momentum is a spatially modulating superconducting energy gap Delta(r), where r is a position. Recently, this concept has been generalized to the pair-density-wave (PDW) state predicted to exist in copper oxides (cuprates)(3,4). Although the signature of a cuprate PDW has been detected in Cooper-pair tunnelling(5), the distinctive signature in singleelectron tunnelling of a periodic Delta(r) modulation has not been observed. Here, using a spectroscopic technique based on scanning tunnelling microscopy, we find strong Delta(r) modulations in the canonical cuprate Bi2Sr2CaCu2O8+delta that have eight-unit-cell periodicity or wavevectors Q approximate to (2 pi/a(0))(1/8, 0) and Q approximate to (2 pi/a(0))(0, 1/8) (where a(0) is the distance between neighbouring Cu atoms). Simultaneous imaging of the local density of states N(r, E) (where E is the energy) reveals electronic modulations with wavevectors Q and 2Q, as anticipated when the PDW coexists with superconductivity. Finally, by visualizing the topological defects in these N(r, E) density waves at 2Q, we find them to be concentrated in areas where the PDW spatial phase changes by pi, as predicted by the theory of half-vortices in a PDW state(6,7). Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in Bi2Sr2CaCu2O8+delta.