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Abstract

The quantum condensate of Cooper pairs forming a superconductor was originally conceived as being translationally invariant. In theory, however, pairs can exist with finite momentum Q, thus generating a state with a spatially modulated Cooper-pair density(1,2). Such a state has been created in ultracold Li-6 gas(3) but never observed directly in any superconductor. It is now widely hypothesized that the pseudogap phase(4) of the copper oxide superconductors contains such a 'pair density wave' state(5-21). Here we report the use of nanometre-resolution scanned Josephson tunnelling microscopy(22-24) to image Cooper pair tunnelling from a d-wave superconducting microscope tip to the condensate of the superconductor Bi2Sr2CaCu2O8+x. We demonstrate condensate visualization capabilities directly by using the Cooper-pair density variations surrounding zinc impurity atoms(25) and at the Bi2Sr2CaCu2O8+x crystal supermodulation(26). Then, by using Fourier analysis of scanned Josephson tunnelling images, we discover the direct signature of a Cooper-pair density modulation at wavevectors Q(P) approximate to (0.25, 0)2 pi/a(0) and (0, 0.25)2 pi/a(0) in Bi2Sr2CaCu2O8+x. The amplitude of these modulations is about five per cent of the background condensate density and their form factor exhibits primarily s or s' symmetry. This phenomenology is consistent with Ginzburg-Landau theory(5,13,14) when a charge density wave(5,27) with d-symmetry form factor(28-30) and wavevector Q(C) = Q(P) coexists with a d-symmetry superconductor; it is also predicted by several contemporary microscopic theories for the pseudogap phase(18-21).