Abstract

Superconductors are quantum fluids and pair density waves are quantum crystals, both being macroscopic quantum states of coherently condensed electron pairs. To visualize and explore these states directly at atomic scale, we have developed scanned Josephson tunneling microscopes (SJTM). Such instruments can image both the single-electron quasiparticles and, in a different mode, the quantum condensate of electron-pairs. Moreover, these instruments can, in the Andreev quasiparticle retroreflection regime, be operated as scanned Andreev tunneling microscopes (SATM). To visualize pair density wave (PDW) states in the conventional spin-singlet superconductor NbSe2, we implemented atomic-resolution SJTM using Nb s-wave scan tips. Here we detect three commensurate PDWs, each whose electron-pair density and energy-gap modulate spatially at the wavevectors 𝑄𝑖=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 states [1].

We searched for a pair density wave in cuprate superconductors using cuprate d-wave scan tips, and discovered a PDW state [2] exhibiting periodic modulations of the electron-pair density [2], the quasiparticle response to the electron-pair crystal [3], and of the associated electron-pair binding energy [3,4]. Most recently, we studied the putative spin-triplet topological superconductor UTe2 using Nb s-wave scan tips, where no Josephson pair current is detectable. However, we can visualize the pairing energy-gap and find three PDWs at incommensurate wavevectors 𝑃𝑖=1,2,3 indistinguishable from the wavevectors 𝑄𝑖=1,2,3 of the prevenient CDW . Every 𝑃𝑖:𝑄𝑖 pair is registered to each other spatially, but with a relative phase 𝛿𝜙≈𝜋. From these observations, this state is the first known spin-triplet PDW [5]. SJTM studies reveal an unexplored frontier of macroscopic quantum physics with great potential for discovery.

References: [1] Science 372, 1447 (2021); [2] Nature 532, 343 (2016); [3] Science 364, 976 (2019); [4] Nature 580, 6570 (2020); [5] Nature (2023) arXiv:2209.10859.