Detection of a Cooper-pair density wave in Bi₂Sr₂CaCu₂O_8+x

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. Such a state has been created in ultracold 6 Li gas but never observed directly in any superconductor. It is now widely hypothesized that the pseudogap phase of the copper oxide superconductors contains such a 'pair density wave' state. Here we report the use of nanometre-resolution scanned Josephson tunnelling microscopy to image Cooper pair tunnelling from a d-wave superconducting microscope tip to the condensate of the superconductor Bi₂Sr₂CaCu₂O_8+x. We demonstrate condensate visualization capabilities directly by using the Cooper-pair density variations surrounding zinc impurity atoms and at the Bi₂Sr₂CaCu₂O_8+x crystal supermodulation. 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 ≈ (0.25, 0)2π/a₀ and (0, 0.25)2π/a₀ in Bi₂Sr₂CaCu₂O_8+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 when a charge density wave with d-symmetry form factor 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.