Fulde, P. & Ferrell, R. A. Superconductivity in a strong spin-exchange field. Phys. Rev. 135, A550 (1964).
Larkin, A. I. & Ovchinnikov, Y. N. Nonuniform state of superconductors. Zh. Eksp. Teor. Fiz. 47, 1136–1146 (1964).
Himeda, A., Kato, T. & Ogata, M. Stripe states with spatially oscillating d-wave superconductivity in the two-dimensional t–t′–J model. Phys. Rev. Lett. 88, 117001 (2002).
Berg, E. et al. Dynamical layer decoupling in a stripe-ordered high-Tc superconductor. Phys. Rev. Lett. 99, 127003 (2007).
Lee, P. A. Amperean pairing and the pseudogap phase of cuprate superconductors. Phys. Rev. X 4, 031017 (2014).
Fradkin, E., Kivelson, S. A. & Tranquada, J. M. Colloquium: Theory of intertwined orders in high temperature superconductors. Rev. Mod. Phys. 87, 457 (2015).
Fernandes, R. M., Orth, P. P. & Schmalian, J. Intertwined vestigial order in quantum materials: nematicity and beyond. Annu. Rev. Condens. Matter Phys. 10, 133–154 (2019).
Agterberg, D. F. et al. The physics of pair-density waves: cuprate superconductors and beyond. Annu. Rev. Condens. Matter Phys. 11, 231–270 (2020).
Hamidian, M. et al. Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x. Nature 532, 343–347 (2016).
Ruan, W. et al. Visualization of the periodic modulation of Cooper pairing in a cuprate superconductor. Nat. Phys. 14, 1178–1182 (2018).
Du, Z. et al. Imaging the energy gap modulations of the cuprate pair-density-wave state. Nature 580, 65–70 (2020).
Liu, X., Chong, Y. X., Sharma, R. & Davis, J. S. Discovery of a Cooper-pair density wave state in a transition-metal dichalcogenide. Science 372, 1447–1452 (2021).
Chen, H. et al. Roton pair density wave in a strong-coupling kagome superconductor. Nature 599, 222–228 (2021).
Wang, S. et al. Scattering interference signature of a pair density wave state in the cuprate pseudogap phase. Nat. Commun. 12, 6087 (2021).
Chen, W. et al. Identification of a nematic pair density wave state in Bi2Sr2CaCu2O8+x. Proc. Natl Acad. Sci. USA 119, e2206481119 (2022).
Gu, Q. et al. Detection of a pair density wave state in UTe2. Nature 618, 921–927 (2023).
Zhao, H. et al. Smectic pair-density-wave order in EuRbFe4As4. Nature 618, 940–945 (2023).
Liu, Y. et al. Pair density wave state in a monolayer high-Tc iron-based superconductor. Nature 618, 934–939 (2023).
Wei, L.-X. et al. Discovery of smectic charge and pair-density-wave orders in topological monolayer 1T′-MoTe2. Preprint at https://arxiv.org/abs/2308.11101 (2023).
Schwemmer, T. et al. Sublattice modulated superconductivity in the kagome Hubbard model. Phys. Rev. B 110, 024501 (2024).
Fernandes, R. M. et al. Iron pnictides and chalcogenides: a new paradigm for superconductivity. Nature 601, 35–44 (2022).
Fernandes, R., Chubukov, A. & Schmalian, J. What drives nematic order in iron-based superconductors? Nat. Phys. 10, 97–104 (2014).
Yin, Z., Haule, K. & Kotliar, G. Kinetic frustration and the nature of the magnetic and paramagnetic states in iron pnictides and iron chalcogenides. Nat. Mater. 10, 932–935 (2011).
Checkelsky, J. G., Bernevig, B. A., Coleman, P., Si, Q. & Paschen, S. Flat bands, strange metals and the Kondo effect. Nat. Rev. Mater. 9, 509–526 (2024).
Lubashevsky, Y., Lahoud, E., Chashka, K., Podolsky, D. & Kanigel, A. Shallow pockets and very strong coupling superconductivity in FeSexTe1−x. Nat. Phys. 8, 309–312 (2012).
Shibauchi, T., Hanaguri, T. & Matsuda, Y. Exotic superconducting states in FeSe-based materials. J. Phys. Soc. Jpn 89, 102002 (2020).
Kong, L. et al. Half-integer level shift of vortex bound states in an iron-based superconductor. Nat. Phys. 15, 1181–1187 (2019).
Hanaguri, T., Niitaka, S., Kuroki, K. & Takagi, H. Unconventional s-wave superconductivity in Fe(Se,Te). Science 328, 474–476 (2010).
Wang, Z. et al. Evidence for dispersing 1D Majorana channels in an iron-based superconductor. Science 367, 104–108 (2020).
Tang, F. et al. Quasi-2D superconductivity in FeTe0.55Se0.45 ultrathin film. J. Phys. Condens. Matter 31, 265702 (2019).
Morfoot, A. B. et al. Resurgence of superconductivity and the role of dxy hole band in FeSe1−xTex. Commun. Phys. 6, 362 (2023).
Chen, M. et al. Direct visualization of sign-reversal s± superconducting gaps in FeTe0.55Se0.45. Phys. Rev. B 99, 014507 (2019).
Cho, D., Bastiaans, K., Chatzopoulos, D., Gu, G. & Allan, M. A strongly inhomogeneous superfluid in an iron-based superconductor. Nature 571, 541–545 (2019).
Lawler, M. et al. Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states. Nature 466, 347–351 (2010).
Fujita, K. et al. Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates. Proc. Natl Acad. Sci. USA 111, E3026–E3032 (2014).
Böhmer, A. E., Chu, J.-H., Lederer, S. & Yi, M. Nematicity and nematic fluctuations in iron-based superconductors. Nat. Phys. 18, 1412–1419 (2022).
Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Zaanen, J. From quantum matter to high-temperature superconductivity in copper oxides. Nature 518, 179–186 (2015).
Ronning, F. et al. Electronic in-plane symmetry breaking at field-tuned quantum criticality in CeRhIn5. Nature 548, 313–317 (2017).
Jiang, K. et al. Kagome superconductors AV3Sb5 (A = K, Rb, Cs). Natl Sci. Rev. 10, nwac199 (2023).
Li, J. et al. Reemergeing electronic nematicity in heavily hole-doped Fe-based superconductors. Preprint at https://arxiv.org/abs/1611.04694 (2016).
Liu, X. et al. Evidence of nematic order and nodal superconducting gap along [110] direction in RbFe2As2. Nat. Commun. 10, 1039 (2019).
Ishida, K. et al. Novel electronic nematicity in heavily hole-doped iron pnictide superconductors. Proc. Natl Acad. Sci. USA 117, 6424–6429 (2020).
Wei, T. et al. Observation of superconducting pair density modulation within lattice unit cell. Chin. Phys. Lett. 42, 027404 (2025).
Zhang, Y., Yang, L., Liu, C., Zhang, W. & Fu, Y.-S. Visualizing uniform lattice-scale pair density wave in single-layer FeSe/SrTiO3 films. Preprint at https://arxiv.org/abs/2406.05693 (2024).
Wen, J. et al. Short-range incommensurate magnetic order near the superconducting phase boundary in Fe1+δTe1−xSex. Phys. Rev. B 80, 104506 (2009).
Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).
Castellanos-Gomez, A. et al. Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping. 2D Mater. 1, 011002 (2014).
Ishida, K. et al. Pure nematic quantum critical point accompanied by a superconducting dome. Proc. Natl Acad. Sci. USA 119, e2110501119 (2022).
Hou, Q., Sun, L., Sun, Y. & Shi, Z. Review of single crystal synthesis of 11 iron-based superconductors. Materials 16, 4895 (2023).
Kuo, H.-H., Chu, J.-H., Palmstrom, J. C., Kivelson, S. A. & Fisher, I. R. Ubiquitous signatures of nematic quantum criticality in optimally doped Fe-based superconductors. Science 352, 958–962 (2016).
Zhao, H. et al. Nematic transition and nanoscale suppression of superconductivity in Fe(Te,Se). Nat. Phys. 17, 903–908 (2021).
Agterberg, D. & Tsunetsugu, H. Dislocations and vortices in pair-density-wave superconductors. Nat. Phys. 4, 639–642 (2008).
Berg, E., Fradkin, E. & Kivelson, S. A. Charge-4e superconductivity from pair-density-wave order in certain high-temperature superconductors. Nat. Phys. 5, 830–833 (2009).
Radzihovsky, L. & Vishwanath, A. Quantum liquid crystals in an imbalanced Fermi gas: fluctuations and fractional vortices in Larkin-Ovchinnikov states. Phys. Rev. Lett. 103, 010404 (2009).
Mross, D. F. & Senthil, T. Spin- and pair-density-wave glasses. Phys. Rev. X 5, 031008 (2015).
Aishwarya, A. et al. Melting of the charge density wave by generation of pairs of topological defects in UTe2. Nat. Phys. 20, 964–969 (2024).
Prozorov, R. et al. Intrinsic pinning on structural domains in underdoped single crystals of Ba(Fe1−xCox)2As2. Phys. Rev. B 80, 174517 (2009).
Rößler, S. et al. Nematic state of the FeSe superconductor. Phys. Rev. B 105, 064505 (2022).
Jenkins, N. et al. Imaging the essential role of spin fluctuations in high-Tc superconductivity. Phys. Rev. Lett. 103, 227001 (2009).
Devarakonda, A. et al. Evidence of striped electronic phases in a structurally modulated superlattice. Nature 631, 526–530 (2024).
Gao, Z.-Q., Lin, Y.-P. & Lee, D.-H. Pair-breaking scattering interference as a mechanism for superconducting gap modulation. Phys. Rev. B 110, 224509 (2024).
Kong, L. et al. Dataset: Cooper-pair density modulation state in an iron-based superconductor. Zenodo https://doi.org/10.5281/zenodo.14523285 (2024).