Spatially modulated superconducting states are typically associated with broken translational symmetry, leading to density-wave orders with wavelengths spanning multiple unit cells. In this talk, I will present a fundamentally different form of superconducting order in which translational symmetry remains intact while intra–unit-cell symmetries are broken, giving rise to a novel pair density modulation (PDM) state [1].

Using scanning tunneling microscopy on exfoliated flakes of the iron-based superconductor FeTeSe, we directly observe a pronounced modulation of the superconducting gap at the lattice periodicity, with an amplitude exceeding 30% of its average value. We show that this effect originates from a strong imbalance in pairing strength between the two nominally equivalent iron sublattices. Supported by theoretical modeling [2], our results point to a mechanism driven by the interplay of sublattice symmetry breaking and a nematic distortion unique to the thin-flake geometry.

These findings establish a new paradigm for superconducting order—distinct from conventional density waves—and highlight the importance of intra–unit-cell degrees of freedom in strongly correlated systems. More broadly, they open new directions for exploring intertwined electronic orders in iron-based superconductors and beyond.

[1] Cooper-pair density modulation state in an iron-based superconductor, Lingyuan Kong, Michał Papaj, Hyunjin Kim, Yiran Zhang, Eli Baum, Hui Li, Kenji Watanabe, Takashi Taniguchi, Genda Gu, Patrick A. Lee, and Stevan Nadj-Perge, Nature 640, 55–61 (2025).

[2] Pair density modulation from glide symmetry breaking and nematic superconductivity, Michał Papaj, Lingyuan Kong, Stevan Nadj-Perge, Patrick A. Lee, Arxiv 2506.19903 (2025).