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# Nematicity and nematic fluctuations in iron-based superconductors

## Abstract

The spontaneous reduction of rotational symmetry in a crystalline solid driven by an electronic mechanism is referred to as electronic nematicity. This phenomenon—initially thought to be rare—has now been observed in an increasing number of strongly interacting systems. In particular, the ubiquitous presence of nematicity in a number of unconventional superconductors suggests its importance in developing a unified understanding of their intricate phase diagrams and superconducting pairing. In this regard, the iron-based superconductors present an ideal material platform to study electronic nematicity. Their nematic transition is pronounced, it can be studied with a wide range of experimental techniques, it is easily tunable, and high-quality samples are widely available. Signatures of nematic quantum criticality near optimal dopings have been reported in almost all families of iron-based superconductors. Here we highlight how the nematic phase in this class of materials can be addressed in its full complexity, encompassing momentum-, time-, energy- and material-dependences. We also discuss a number of important open questions that pertain to how nematicity affects the superconducting pairing and normal-state properties, and intriguing quantum-critical behaviour near the nematic transition.

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## References

1. Fradkin, E., Kivelson, S. A., Lawler, M. J., Eisenstein, J. P. & Mackenzie, A. P. Nematic Fermi fluids in condensed matter physics. Annu. Rev. Condens. Matter Phys. 1, 153–178 (2010).

2. Lilly, M. P., Cooper, K. B., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Evidence for an anisotropic state of two-dimensional electrons in high Landau levels. Phys. Rev. Lett. 82, 394–397 (1999).

3. Borzi, R. A. et al. Formation of a nematic fluid at high fields in Sr3Ru2O7. Science 315, 214–217 (2007).

4. Lester, C. et al. Field-tunable spin-density-wave phases in Sr3Ru2O7. Nat. Mater. 14, 373–378 (2015).

5. Hinkov, V. et al. Electronic liquid crystal state in the high-temperature superconductor YBa2Cu3O6.45. Science 319, 597–600 (2008).

6. de la Cruz, C. et al. Magnetic order close to superconductivity in the iron-based layered LaO1 − xFxFeAs systems. Nature 453, 899–902 (2008).

7. Nomura, T. et al. Crystallographic phase transition and high-Tc superconductivity in LaFeAsO:F. Superconductor Sci. Technol. 21, 125028 (2008).

8. Fernandes, R. M. et al. Effects of nematic fluctuations on the elastic properties of iron arsenide superconductors. Phys. Rev. Lett. 105, 157003 (2010).

9. Nandi, S. et al. Anomalous suppression of the orthorhombic lattice distortion in superconducting Ba(Fe1–xCox)2 As2 single crystals. Phys. Rev. Lett. 104, 057006 (2010).

10. Chu, J.-H., Kuo, H.-H., Analytis, J. G. & Fisher, I. R. Divergent nematic susceptibility in an iron arsenide superconductor. Science 337, 710–712 (2012).

11. Chu, J.-H. et al. In-plane resistivity anisotropy in an underdoped iron arsenide superconductor. Science 329, 824–826 (2010).

12. Dusza, A. et al. Anisotropic charge dynamics in detwinned Ba(Fe1–xCox)2As2. Europhys. Lett. 93, 37002 (2011).

13. Fu, M. et al. NMR search for the spin nematic state in a LaFeAsO single crystal. Phys. Rev. Lett. 109, 247001 (2012).

14. Jiang, S., Jeevan, H. S., Dong, J. & Gegenwart, P. Thermopower as a sensitive probe of electronic nematicity in iron pnictides. Phys. Rev. Lett. 110, 067001 (2013).

15. Chuang, T.-M. et al. Nematic Electronic Structure in the ‘Parent’ State of the Iron-Based Superconductor Ca(Fe1–xCox)2As2. Science 327, 181–184 (2010).

16. Lu, X. et al. Nematic spin correlations in the tetragonal state of uniaxial-strained BaFe2–xNixAs2. Science 345, 657–660 (2014).

17. Lu, X. et al. Spin-excitation anisotropy in the nematic state of detwinned FeSe. Nat. Phys. 18, 806–812 (2021).

18. Kasahara, S. et al. Electronic nematicity above the structural and superconducting transition in BaFe2(As1 − xP2)2. Nature 486, 382–385 (2012).

19. Rosenthal, E. P. et al. Visualization of electron nematicity and unidirectional antiferroic fluctuations at high temperatures in NaFeAs. Nat. Phys. 10, 225–232 (2014).

20. Wiecki, P. et al. NMR evidence for static local nematicity and its cooperative interplay with low-energy magnetic fluctuations in FeSe under pressure. Phys. Rev. B 96, 180502 (2017).

21. Thewalt, E. et al. Imaging anomalous nematic order and strain in optimally doped BaFe2(As,P)2. Phys. Rev. Lett. 121, 027001 (2018).

22. Shimojima, T. et al. Discovery of mesoscopic nematicity wave in iron-based superconductors. Science 373, 1122–1125 (2021).

23. Lahiri, A., Klein, A. & Fernandes, R. M. Defect-induced electronic smectic state at the surface of nematic materials. Phys. Rev. B 106, L140503 (2021).

24. Yi, M. et al. Symmetry-breaking orbital anisotropy observed for detwinned Ba(Fe1 − xCox)2As2 above the spin density wave transition. Proc. Natl Acad. Sci. USA 108, 6878–6883 (2011).

25. Zhang, Y. et al. Symmetry breaking via orbital-dependent reconstruction of electronic structure in detwinned NaFeAs. Phys. Rev. B 85, 085121 (2012).

26. Suzuki, Y. et al. Momentum-dependent sign inversion of orbital order in superconducting FeSe. Phys. Rev. B 92, 205117 (2015).

27. Zhang, Y. et al. Distinctive orbital anisotropy observed in the nematic state of a FeSe thin film. Phys. Rev. B 94, 115153 (2016).

28. Pfau, H. et al. Momentum dependence of the nematic order parameter in iron-based superconductors. Phys. Rev. Lett. 123, 066402 (2019).

29. Watson, M. D. et al. Evidence for unidirectional nematic bond ordering in FeSe. Phys. Rev. B 94, 201107 (2016).

30. Yi, M. et al. The nematic energy scale and the missing electron pocket in FeSe. Phys. Rev. X 9, 041049 (2019).

31. Rhodes, L. C., Eschrig, M., Kim, T. K. & Watson, M. D. FeSe and the missing electron pocket problem. Front. Phys. 10, 859017 (2022).

32. Yi, M. et al. Dynamic competition between spin–density wave order and superconductivity in underdoped Ba1 − xKxFe2As2. Nat. Commun. 5, 3711 (2014).

33. Tanatar, M. A. et al. Uniaxial-strain mechanical detwinning of CaFe2As2 and BaFe2As2 crystals: optical and transport study. Phys. Rev. B 81, 184508 (2010).

34. 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).

35. Böhmer, A. E. et al. Nematic susceptibility of hole-doped and electron-doped BaFe2As2 iron-based superconductors from shear modulus measurements. Phys. Rev. Lett. 112, 047001 (2014).

36. Böhmer, A. E. & Meingast, C. Electronic nematic susceptibility of iron-based superconductors. Comptes Rendus Phys. 17, 90–112 (2016).

37. Gallais, Y. & Paul, I. Charge nematicity and electronic Raman scattering in iron-based superconductors. Comptes Rendus Phys. 17, 113–139 (2016).

38. Chen, X., Maiti, S., Fernandes, R. M. & Hirschfeld, P. J. Nematicity and superconductivity: competition versus cooperation. Phys. Rev. B 102, 184512 (2020).

39. Edelberg, D., Kumar, H., Shenoy, V., Ochoa, H. & Pasupathy, A. N. Tunable strain soliton networks confine electrons in van der Waals materials. Nat. Phys. 16, 1097–1102 (2020).

40. Kissikov, T. et al. Uniaxial strain control of spin-polarization in multicomponent nematic order of BaFe2As2. Nat. Commun. 9, 1058 (2018).

41. Caglieris, F. et al. Strain derivative of thermoelectric properties as a sensitive probe for nematicity. npj Quantum Mater. 6, 27 (2021).

42. Sanchez, J. J. et al. The transport–structural correspondence across the nematic phase transition probed by elasto X-ray diffraction. Nat. Mater. 20, 1519–1524 (2021).

43. Ikeda, M. S. et al. Elastocaloric signature of nematic fluctuations. Proc. Natl Acad. Sci. USA 118, e2105911118 (2021).

44. Hosoi, S. et al. Nematic quantum critical point without magnetism in FeSe1 − xSx superconductors. Proc. Natl Acad. Sci. USA 113, 8139–8143 (2016).

45. Hong, X. et al. Evolution of the nematic susceptibility in LaFe1 − xCoxAsO. Phys. Rev. Lett. 125, 067001 (2020).

46. Ishida, K. et al. Pure nematic quantum critical point accompanied by a superconducting dome. Proc. Natl Acad. Sci. USA 119, e2110501119 (2022).

47. Worasaran, T. et al. Nematic quantum criticality in an Fe-based superconductor revealed by strain-tuning. Science 372, 973–977 (2021).

48. Metzner, W., Rohe, D. & Andergassen, S. Soft Fermi surfaces and breakdown of Fermi-liquid behavior. Phys. Rev. Lett. 91, 066402 (2003).

49. Lederer, S., Schattner, Y., Berg, E. & Kivelson, S. A. Enhancement of superconductivity near a nematic quantum critical point. Phys. Rev. Lett. 114, 097001 (2015).

50. Yamase, H. & Zeyher, R. Superconductivity from orbital nematic fluctuations. Phys. Rev. B 88, 180502 (2013).

51. Maier, T. A. & Scalapino, D. J. Pairing interaction near a nematic quantum critical point of a three-band CuO2 model. Phys. Rev. B 90, 174510 (2014).

52. Metlitski, M. A., Mross, D. F., Sachdev, S. & Senthil, T. Cooper pairing in non-Fermi liquids. Phys. Rev. B 91, 115111 (2015).

53. Lederer, S., Schattner, Y., Berg, E. & Kivelson, S. A. Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point. Proc. Natl Acad. Sci. USA 114, 4905–4910 (2017).

54. Labat, D. & Paul, I. Pairing instability near a lattice-influenced nematic quantum critical point. Phys. Rev. B 96, 195146 (2017).

55. Chubukov, A. V., Abanov, A., Wang, Y. & Wu, Y.-M. The interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. Ann. Phys. 417, 168142 (2020).

56. Lawler, M. J., Barci, D. G., Fernández, V., Fradkin, E. & Oxman, L. Nonperturbative behavior of the quantum phase transition to a nematic Fermi fluid. Phys. Rev. B 73, 085101 (2006).

57. Metlitski, M. A. & Sachdev, S. Quantum phase transitions of metals in two spatial dimensions. I. Ising-nematic order. Phys. Rev. B 82, 075127 (2010).

58. Mross, D. F., McGreevy, J., Liu, H. & Senthil, T. Controlled expansion for certain non-Fermi-liquid metals. Phys. Rev. B 82, 045121 (2010).

59. Lee, W.-C. & Phillips, P. W. Non-Fermi liquid due to orbital fluctuations in iron pnictide superconductors. Phys. Rev. B 86, 245113 (2012).

60. Fitzpatrick, A. L., Kachru, S., Kaplan, J. & Raghu, S. Non-Fermi-liquid fixed point in a Wilsonian theory of quantum critical metals. Phys. Rev. B 88, 125116 (2013).

61. Dalidovich, D. & Lee, S.-S. Perturbative non-Fermi liquids from dimensional regularization. Phys. Rev. B 88, 245106 (2013).

62. Shibauchi, T., Carrington, A. & Matsuda, Y. A quantum critical point lying beneath the superconducting dome in iron pnictides. Annu. Rev. Condens. Matter Phys. 5, 113–135 (2014).

63. Analytis, J. G. et al. Transport near a quantum critical point in BaFe2(As1–xPx)2. Nat. Phys. 10, 194–197 (2014).

64. Licciardello, S. et al. Electrical resistivity across a nematic quantum critical point. Nature 567, 213–217 (2019).

65. Shimojima, T. et al. Ultrafast nematic-orbital excitation in FeSe. Nat. Commun. 10, 1946 (2019).

66. Fang, C., Yao, H., Tsai, W.-F., Hu, J. & Kivelson, S. A. Theory of electron nematic order in LaFeAsO. Phys. Rev. B 77, 224509 (2008).

67. Baek, S.-H. et al. Orbital-driven nematicity in FeSe. Nat. Mater. 14, 210–214 (2015).

68. Wang, Q. et al. Strong interplay between stripe spin fluctuations, nematicity and superconductivity in FeSe. Nat. Mater. 15, 159–163 (2016).

69. Böhmer, A. E. & Kreisel, A. Nematicity, magnetism and superconductivity in FeSe. J. Phys. Condens. Matter 30, 023001 (2018).

70. Lee, C.-C., Yin, W.-G. & Ku, W. Ferro-orbital order and strong magnetic anisotropy in the parent compounds of iron-pnictide superconductors. Phys. Rev. Lett. 103, 267001 (2009).

71. Onari, S. & Kontani, H. Self-consistent vertex correction analysis for iron-based superconductors: mechanism of coulomb interaction-driven orbital fluctuations. Phys. Rev. Lett. 109, 137001 (2012).

72. Gastiasoro, M. N., Paul, I., Wang, Y., Hirschfeld, P. J. & Andersen, B. M. Emergent defect states as a source of resistivity anisotropy in the nematic phase of iron pnictides. Phys. Rev. Lett. 113, 127001 (2014).

73. Fernandes, R. M., Abrahams, E. & Schmalian, J. Anisotropic in-plane resistivity in the nematic phase of the iron pnictides. Phys. Rev. Lett. 107, 217002 (2011).

74. Valenzuela, B., Bascones, E. & Calderón, M. J. Conductivity anisotropy in the antiferromagnetic state of iron pnictides. Phys. Rev. Lett. 105, 207202 (2010).

75. de Carvalho, V. S. & Fernandes, R. M. Resistivity near a nematic quantum critical point: impact of acoustic phonons. Phys. Rev. B 100, 115103 (2019).

76. Kuo, H. & Fisher, I. R. Effect of disorder on the resistivity anisotropy near the electronic nematic phase transition in pure and electron-doped BaFe2As2. Phys. Rev. Lett. 112, 227001 (2014).

77. Tanatar, M. A. et al. Origin of the resistivity anisotropy in the nematic phase of FeSe. Phys. Rev. Lett. 117, 127001 (2016).

78. Mirri, C. et al. Origin of the resistive anisotropy in the electronic nematic phase of BaFe2As2 revealed by optical spectroscopy. Phys. Rev. Lett. 115, 107001 (2015).

79. Malinowski, P. et al. Suppression of superconductivity by anisotropic strain near a nematic quantum critical point. Nat. Phys. 16, 1189–1193 (2020).

80. Wang, L. et al. Superconductivity-enhanced nematicity and ‘s + d’ gap symmetry in Fe(Se1–xSx). Phys. Status Solidi b 254, 1600153 (2017).

81. Sprau, P. O. et al. Discovery of orbital-selective Cooper pairing in FeSe. Science 357, 75–80 (2017).

82. Hanaguri, T. et al. Two distinct superconducting pairing states divided by the nematic end point in FeSe1–xSx. Sci. Adv. 4, eaar6419 (2018).

83. Paul, I. & Garst, M. Lattice effects on nematic quantum criticality in metals. Phys. Rev. Lett. 118, 227601 (2017).

84. Reiss, P., Graf, D., Haghighirad, A. A., Vojta, T. & Coldea, A. I. Signatures of a quantum Griffiths phase close to an electronic nematic quantum phase transition. Phys. Rev. Lett. 127, 246402 (2021).

85. Rosenberg, E. W., Chu, J.-H., Ruff, J. P. C., Hristov, A. T. & Fisher, I. R. Divergence of the quadrupole-strain susceptibility of the electronic nematic system YbRu2Ge2. Proc. Natl Acad. Sci. USA 116, 7232–7237 (2019).

86. Cao, Y. et al. Nematicity and competing orders in superconducting magic-angle graphene. Science 372, 264–271 (2021).

87. Yonezawa, S. Nematic superconductivity in doped Bi2Se3 topological superconductors. Condens. Matter 4, 2 (2019).

88. Kohama, Y. et al. Possible observation of quantum spin-nematic phase in a frustrated magnet. Proc. Natl Acad. Sci. USA 116, 10686–10690 (2019).

89. Seo, S. et al. Nematic state in CeAuSb2. Phys. Rev. X 10, 011035 (2020).

90. Eckberg, C. et al. Sixfold enhancement of superconductivity in a tunable electronic nematic system. Nat. Phys. 16, 346–350 (2020).

91. Chibani, S. et al. Lattice-shifted nematic quantum critical point in FeSe1–xSx. npj Quantum Mater. 6, 37 (2020).

## Acknowledgements

We would like to thank I. Fisher and Q. Si for valuable comments and A. Kreyssig for critical and helpful reading of this manuscript. A.E.B. acknowledges support from the German Research Foundation (DFG) under CRC/TRR 288 (Project A02) and from the Helmholtz Association under contract no. VH-NG-1242. J.H.C. acknowledges the support of the Gordon and Betty Moore Foundation’s EPiQS Initiative, grant no. GBMF6759 to J.-H.C., the David and Lucile Packard Foundation, and the US Air Force Office of Scientific Research under grant no. FA9550-21-1-0068. S.L. is supported by the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator (QSA). M.Y. acknowledges support from the US Department of Energy grant no. DE-SC0021421, the Robert A. Welch Foundation grant no. C-2024, and the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant no. GBMF9470.

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Böhmer, A.E., Chu, JH., Lederer, S. et al. Nematicity and nematic fluctuations in iron-based superconductors. Nat. Phys. 18, 1412–1419 (2022). https://doi.org/10.1038/s41567-022-01833-3

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