Visualization of the periodic modulation of Cooper pairing in a cuprate superconductor

In cuprate superconductors, the existence of various intertwined orders associated with spin, charge and Cooper pairs 1 , 2 is an obstacle in understanding the mechanism of Cooper pairing. The ubiquitous charge order is particularly important 2 – 7 . Various theories have been proposed to explain the origin of the charge order and its implications for the superconducting phase, including charge stripes 8 , electronic nematicity 8 , 9 and Fermi surface instability 5 , 10 . A highly appealing physical picture is the ‘pair density wave’, a spatially periodic modulation of Cooper pairing, which may also induce a charge order 2 , 11 – 21 . To elucidate the existence and nature of the pair density wave, we use scanning tunnelling microscopy to investigate a severely underdoped cuprate, in which superconductivity just emerges on top of a pronounced chequerboard charge order. We observe a periodic modulation of both the superconducting coherence peak and gap depth, indicating the existence of a density wave order of Cooper pairing based on the empirical relationship between superconducting coherence and superfluid density 22 – 27 . The pair density wave has the same spatial periodicity as the charge order, and the amplitudes of the two orders exhibit clear positive correlation. These results shed new light on the origin of and interplay between the charge order and Cooper pairing modulation in the cuprates. A periodic pattern of Cooper pairs is observed at the atomic scale and is shown to be correlated with the local strength of the superconductivity. This reveals a new interplay between different ordered states in the cuprates.