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 density1,2. Such a state has been created in ultracold 6Li gas3 but never observed directly in any superconductor. It is now widely hypothesized that the pseudogap phase4 of the copper oxide superconductors contains such a ‘pair density wave’ state5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21. Here we report the use of nanometre-resolution scanned Josephson tunnelling microscopy22,23,24 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 atoms25 and at the Bi2Sr2CaCu2O8+x crystal supermodulation26. Then, by using Fourier analysis of scanned Josephson tunnelling images, we discover the direct signature of a Cooper-pair density modulation at wavevectors QP ≈ (0.25, 0)2π/a0 and (0, 0.25)2π/a0 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 theory5,13,14 when a charge density wave5,27 with d-symmetry form factor28,29,30 and wavevector QC = QP coexists with a d-symmetry superconductor; it is also predicted by several contemporary microscopic theories for the pseudogap phase18,19,20,21.
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Acknowledgements
We acknowledge and thank D. Agterberg, A. V. Balatsky, D. Chowdhury, A. Chubukov, E. Fradkin, R. Hulet, S. A. Kivelson, P. A. Lee, M. Norman, J. W. Orenstein, C. Pepin, S. Sachdev, J. Tranquada and Y. Wang for discussions and advice. The development and operation of HTS SJTM technology and M.H.H. and A.K. were funded by the Moore Foundation’s EPiQS Initiative through grant number GBMF4544. S.D.E. acknowledges studentship funding from the EPSRC under grant number EP/G03673X/1. J.C.S.D. and A.P.M. acknowledge research support from the EPSRC through the grant programme ‘Topological Protection and Non-Equilibrium States in Correlated Electron Systems’. S.U. and H.E. acknowledge support from a Grant-in-Aid for Scientific Research from the Ministry of Science and Education (Japan). S.H.J. and J.L. acknowledge support from the Institute for Basic Science, Korea under grant number IBS-R009-D1. J.C.S.D. and K.F. acknowledge salary support from the US Department of Energy, Office of Basic Energy Sciences, under contract number DEAC02-98CH10886. E.-A.K. acknowledges support from the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under award DE-SC0010313.
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M.H.H., S.D.E., A.K., and J.L. developed the SJTM techniques and carried out the experiments. K.F., H.E. and S.U. synthesized and characterized the samples. M.H.H., S.D.E., A.K., S.H.J. and K.F. developed and carried out analyses. E.-A.K. and M.J.L. provided theoretical guidance. A.P.M., J.L. and J.C.S.D. supervised the project and wrote the paper with key contributions from M.H.H., S.D.E. and K.F. The manuscript reflects the contributions and ideas of all authors.
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Extended data figures and tables
Extended Data Figure 1 SJTM circuit model and phase diffusion dynamics.
a, Circuit diagram of the hybrid spectroscopic-imaging STM/SJTM setup used in these experiments. The voltage source V is from the usual STM bias controller; the load resistor RB = 10 MΩ; the single-particle tunnelling resistance of the Josephson junction formed between the tip and sample is RN, and the voltage actually developed across the junction is VJJ. b, The dynamics of this circuit produces two predominant effects. First there is a sudden change in the I(V) characteristic measured with the external ammeter shown, when the current reaches a value 
where IJ is the zero-temperature Josephson critical current and T* is an effective temperature parameterizing the dissipative environment of the junction. The second predicted effect is strong hysteresis depending on which direction the external voltage is swept; this is shown as the difference between the solid-red and dashed-blue lines. Both effects are seen very clearly and universally in the measured I(V) throughout our studies reported here. c, The relationship of the current as in b but in terms of the voltage across the Josephson junction VJJ. d, The dashed curve represents a typical dI/dV spectrum on as-grown BSCCO sample, measured using a normal metallic tungsten tip. The solid line is a simulation for an expected dI/dV spectrum when using a BSCCO superconducting tip; we use the standard equation for tunnelling between two superconductors, each with the density of states identical to the dashed line. The result, in very good agreement with the typical measured SIS spectrum, is shown in Fig. 2b.
Extended Data Figure 2 Spectroscopic/topographic data from two distinct BSCCO tips.
Typical dI/dV spectrum, topography and magnitude of its Fourier transform 
measured with two completely distinct BSCCO tips on two different BSCCO samples: tip 1 (a, c and e) and tip 2 (b, d and f).
Extended Data Figure 3 Simulation of topography with BSCCO nanoflake tip.
a, Surface topography T( r ) of BSCCO sample; image obtained with a conventional metallic tungsten tip. b, Magnitude of Fourier transform (FT) of a. c, Model for BSCCO nanoflake tip that is aligned with the BSCCO surface in a. d, Model for BSCCO nanoflake tip that is misaligned with the BSCCO surface in a. e, Convolution of BSCCO surface image in a and aligned BSCCO nanoflake tip in c. Inset shows resultant Fourier Transform with Bragg peaks in the corners and supermodulation peaks. f, Convolution of BSCCO surface image in a and misaligned BSCCO nanoflake tip in d. Inset shows resulting Fourier transform with many additional broad peaks caused by moiré pattern effects. Comparison to e demonstrates that the tip used in the studies reported here was well aligned with the sample.
Extended Data Figure 4 Spatial variation of HTS tip–sample Josephson junction I(V).
a, A histogram of all Ic values measured at different locations in the field of view shown in Fig. 3b. The characteristic Ic values associated with the three spectra in b are indicated by the coloured arrows. b, Three I(V) formed by averaging the constituent I(V) from the bins indicated by the coloured arrows in a. They demonstrate the variation in the measured I(V) characteristic that occurs at different locations in the field of view shown in Fig. 3b. The three Ic values are indicated by coloured arrows.
Extended Data Figure 5 Repeatable utility of BSCCO nanoflake tips for Ic( r ) mapping.
Three Ic( r ) images a, b and c measured with the same BSCCO nanoflake tip, at different times (separated by many days) and using different Josephson junction parameters, but closely related in fields of view. Repeatability and fidelity of our Ic( r ) imaging by SJTM is evident.
Extended Data Figure 6 Sequence of measured Ic( r ) along line in Extended Data Fig. 5b.
Nine individual I(V) spectra measured at the locations indicated by numbers 1–9 in Extended Data Fig. 5b. In each case the transition from the SIS resistive branch to the phase diffusion Josephson tunnelling branch is evident. Moreover, as the sequence passes through the site of a Zn atom, the value of Ic diminishes by ~95% from its maximum, as expected from muon spin rotation experiments. Bias, VB.
Extended Data Figure 7 Before and after topographic images bracketing Ic( r ) map.
a, Topograph taken with BSCCO tip before typical Ic( r ) SJTM map. b, Topograph taken with same BSCCO tip after the same Ic( r ) SJTM map as a. Comparison of a and b shows that tip and surface are very well preserved in our SJTM protocol.
Extended Data Figure 8 Comparison of modulations in Ic( r ) and RN( r ).
a, A typical measured Ic( r ) image of Bi2Sr2CaCu2O8+x with the crystal supermodulation effect retained and apparent as strong spatial modulations in Ic along the vertical axis. b, Measured RN( r ) image simultaneous with a, with the crystal supermodulation effect retained. The spatial modulations in RN( r ) along the vertical axis are greatly diminished in relative amplitude compared to Ic( r ) modulations in a. c, Inset shows 
, the magnitude of the Fourier transform of RN( r ) from b. Plotting the simultaneously measured Fourier amplitudes of 
and 
along the (1, 1) direction passing through the wavevector of the supermodulation QSM shows that modulations in 
are negligible. Therefore the predominant effect in the Ic( r )RN( r ) studied through this work is caused by the Ic( r ) variations, coming from the superfluid density variations 
of the condensate in the sample.
Extended Data Figure 9 d-symmetry density wave 
from topography.
from topography.a, High-resolution topographic image of typical BiO surface at the same hole-density as the Ic( r ) studies, measured at V = 100 meV. b, High-resolution topographic image of identical (registered for every atom within about 10 picometres) BiO surface as a measured at V = −100 meV. c, Difference between a and b; a CDW exhibits its signature logarithmically in such an image and therefore it can be used to detect the d-symmetry form factor density wave, as in Fig. 4d of the main text.
Extended Data Figure 10 Absence CDW setup effect in Ic( r ).
a, 
, the Fourier transform magnitude of the sublattice-resolved image Ox( r ) + Oy( r ) derived from δT( r ), the difference between the two unprocessed topographic images T( r, ±100 meV) in Extended Data Fig. 9. We see directly that the actual modulations in topography due to the density of states modulations from the CDW occur at wavevectors (1 ± 0.22, 0)2π/a0 and (0, 1 ± 0.22)2π/a0 (dashed circles), as has been reported extensively in the past. These only become detectable at the actual CDW wavevector QC = (0.22, 0)2π/a0 and (0, 0.22)2π/a0 when one uses a measure of d-symmetry form factor modulations: 
, as shown in Fig. 4d. Because the physically real modulations in topography and conductance imaging therefore occur at Q = (0.78, 0)2π/a0 and (0, 0.78)2π/a0 (dashed circles), it is impossible for them to produce, through a ‘setup effect’, spurious Ic( r ) modulations at the PDW wavevector QP ≈ (0.25, 0)2π/a0 and (0, 0.25)2π/a0, as indicated by dashed circles in b. b, The measured q -space structure 
(which samples all sublattices in the conventional form
. The PDW maxima occur at QP ≈ (0.25, 0)2π/a0 and (0, 0.25)2π/a0.
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Hamidian, M., Edkins, S., Joo, S. et al. Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x. Nature 532, 343–347 (2016). https://doi.org/10.1038/nature17411
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DOI: https://doi.org/10.1038/nature17411
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