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A superconducting quantum crystal consisting of electron-pairs whose density modulates periodically at wavevector QP, is now referred to as a Pair Density Wave (PDW) state. Although originally mooted in 1964, such states had never been observed directly in any material. To search for a PDW state in cuprate superconductors we developed atomic resolution Scanned Josephson Tunneling Microscopy (SJTM). This new form of quantum microscopy can image both the single-electron quasiparticles and, in a different mode, the quantum condensate of electron-pairs. By using SJTM we detected the cuprate PDW state1 exhibiting periodic modulations of the electron-pair density1 at wavevector Q_P, the quasiparticle response to the electron-pair crystal2, and of the associated electron-pair binding energy2,3. To search for such states in the conventional s-wave superconductor NbSe2, we developed high-speed atomic-resolution SJTM. We detected three PDWs, each whose electron-pair density and energy-gap modulate spatially at the wavevectors Q_(i=1,2,3) of the preexisting charge density wave (CDW) state, but with a global δΦ≅±2π/3 phase difference between the PDW and CDW states4. Most recently, in the topological superconductor UTe2 we visualize the pairing energy-gap with μV-scale energy-resolution made possible by our superconductive SJTM tips. In UTe2 we discovered three PDWs at incommensurate wavevectors P_(i=1,2,3) that are indistinguishable from the wavevectors Q_(i=1,2,3) of the prevenient CDW. Concurrent visualization of the PDWs and the CDWs reveals that every P_i 〖:Q〗_i pair is registered to each other spatially, but with a relative phase δϕ≈π. From these observations, and given UTe2 as a spin-triplet superconductor, this state should be a spin-triplet PDW. While such states do exist in superfluid 3He, for superconductors they are unprecedented.

References

[1] Nature 532, 343 (2016)

[2] Science 364, 976 (2019)

[3] Nature 580, 6570 (2020)

[4] Science 372, 1447 (2021)

[5]  arXiv:2209.10859 (2022)