A first-principle perspective on electronic nematicity in FeSe
Source abstract
Abstract
Abstract Electronic nematicity is an important order in most iron-based superconductors, and FeSe represents a special example, in which nematicity disentangles from spin ordering. A first-principle description of this order remains elusive. Here, we show that by carefully searching the paramagnetic energy landscape within the density functional theory, a nematic solution stands out at either the +U or hybrid functional level with the lowest energy. The band structure and Fermi surface can be well compared with the recent experimental results. Symmetry analysis assigns the dominant order parameter to the Eu irreducible representations of the D4h point group. Distinct from the B1g Ising nematicity as widely discussed in the context of vestigial stripe antiferromagnetic order, the two-component Eu vector order features mixing of the Fe d-orbitals and inversion symmetry breaking, which lead to striking experimental consequences, e.g., missing of an electron pocket.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Iron-based superconductors research · Rare-earth and actinide compounds · Advanced Condensed Matter Physics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (71)
Show source-provided references
1. Wang, N. L., Hosono, H. & Dai, P. Iron-based Superconductors: Materials, Properties and Mechanisms (CRC Press, 2012).10.1201/b13727 ↗
2. Johnson, P. D., Xu, G. & Yin, W.-G. Iron-based Superconductivity, vol. 211 (Springer, 2015).10.1007/978-3-319-11254-1 ↗
3. Richard, P., Sato, T., Nakayama, K., Takahashi, T. & Ding, H. Fe-based superconductors: an angle-resolved photoemission spectroscopy perspective. Rep. Prog. Phys. 74, 124512 (2011).10.1088/0034-4885/74/12/124512 ↗
4. Dai, P., Hu, J. & Dagotto, E. Magnetism and its microscopic origin in iron-based high-temperature superconductors. Nat. Phys. 8, 709–718 (2012).10.1038/nphys2438 ↗
5. 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).10.1038/nmat3120 ↗
6. Yin, Z., Haule, K. & Kotliar, G. Magnetism and charge dynamics in iron pnictides. Nat. Phys. 7, 294–297 (2011).10.1038/nphys1923 ↗
7. Fernandes, R. M., Chubukov, A. V. & Schmalian, J. What drives nematic order in iron-based superconductors? Nat. Phys. 10, 97–104 (2014).10.1038/nphys2877 ↗
8. Fedorov, A. et al. Effect of nematic ordering on electronic structure of FeSe. Sci. Rep. 6, 36834 (2016).
9. 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).10.1126/science.1221713 ↗
10. 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).10.1103/PhysRevB.77.224509 ↗
11. Xu, C., Müller, M. & Sachdev, S. Ising and spin orders in the iron-based superconductors. Phys. Rev. B 78, 020501(R) (2008).10.1103/PhysRevB.78.020501 ↗
12. Fernandes, R., Chubukov, A., Knolle, J., Eremin, I. & Schmalian, J. Preemptive nematic order, pseudogap, and orbital order in the iron pnictides. Phys. Rev. B 85, 024534 (2012).10.1103/PhysRevB.85.024534 ↗
13. 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).10.1103/PhysRevLett.103.267001 ↗
14. Chen, C.-C. et al. Orbital order and spontaneous orthorhombicity in iron pnictides. Phys. Rev. B 82, 100504(R) (2010).10.1103/PhysRevB.82.100504 ↗
15. Kontani, H., Saito, T. & Onari, S. Origin of orthorhombic transition, magnetic transition, and shear-modulus softening in iron pnictide superconductors: analysis based on the orbital fluctuations theory. Phys. Rev. B 84, 024528 (2011).10.1103/PhysRevB.84.024528 ↗
16. Ma, M. et al. Prominent role of spin-orbit coupling in FeSe revealed by inelastic neutron scattering. Phys. Rev. X 7, 021025 (2017).
17. Anisimov, V. I., Aryasetiawan, F. & Lichtenstein, A. First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+U method. J. Phys. Condens. Matter 9, 767–808 (1997).10.1088/0953-8984/9/4/002 ↗
18. Becke, A. D. A new mixing of Hartree-Fock and local density-functional theories. J. Chem. Phys. 98, 1372–1377 (1993).10.1063/1.464304 ↗
19. Bendele, M. et al. Coexistence of superconductivity and magnetism in FeSe1−x under pressure. Phys. Rev. B 85, 064517 (2012).10.1103/PhysRevB.85.064517 ↗
20. Sun, J. et al. Dome-shaped magnetic order competing with high-temperature superconductivity at high pressures in FeSe. Nat. Commun. 7, 12146 (2016).
21. Qing-Yan, W. et al. Interface-induced high-temperature superconductivity in single unit-cell FeSe films on SrTiO3. Chin. Phys. Lett. 29, 037402 (2012).10.1088/0256-307X/29/3/037402 ↗
22. Ge, J.-F. et al. Superconductivity above 100 K in single-layer FeSe films on doped SrTiO3. Nat. Mater. 14, 285–289 (2015).10.1038/nmat4153 ↗
23. Nakayama, K. et al. Reconstruction of band structure induced by electronic nematicity in an FeSe superconductor. Phys. Rev. Lett. 113, 237001 (2014).10.1103/PhysRevLett.113.237001 ↗
24. Shimojima, T. et al. Lifting of xz/yz orbital degeneracy at the structural transition in detwinned FeSe. Phys. Rev. B 90, 121111(R) (2014).10.1103/PhysRevB.90.121111 ↗
25. Suzuki, Y. et al. Momentum-dependent sign inversion of orbital order in superconducting FeSe. Phys. Rev. B 92, 205117 (2015).10.1103/PhysRevB.92.205117 ↗
26. Zhang, P. et al. Observation of two distinct dxz/dyz band splittings in FeSe. Phys. Rev. B 91, 214503 (2015).10.1103/PhysRevB.91.214503 ↗
27. Watson, M. et al. Emergence of the nematic electronic state in FeSe. Phys. Rev. B 91, 155106 (2015).10.1103/PhysRevB.91.155106 ↗
28. Watson, M. et al. Evidence for unidirectional nematic bond ordering in FeSe. Phys. Rev. B 94, 201107(R) (2016).10.1103/PhysRevB.94.201107 ↗
29. Watson, M. D., Haghighirad, A. A., Rhodes, L. C., Hoesch, M. & Kim, T. K. Electronic anisotropies revealed by detwinned angle-resolved photo-emission spectroscopy measurements of FeSe. New J. Phys. 19, 103021 (2017).10.1088/1367-2630/aa8a04 ↗
30. Rhodes, L. C. et al. Scaling of the superconducting gap with orbital character in FeSe. Phys. Rev. B 98, 180503(R) (2018).10.1103/PhysRevB.98.180503 ↗
31. Xu, H. et al. Highly anisotropic and twofold symmetric superconducting gap in nematically ordered FeSe0.93S0.07. Phys. Rev. Lett. 117, 157003 (2016).10.1103/PhysRevLett.117.157003 ↗
32. Zhang, Y. et al. Distinctive orbital anisotropy observed in the nematic state of a FeSe thin film. Phys. Rev. B 94, 115153 (2016).10.1103/PhysRevB.94.115153 ↗
33. Fanfarillo, L. et al. Orbital-dependent Fermi surface shrinking as a fingerprint of nematicity in FeSe. Phys. Rev. B 94, 155138 (2016).10.1103/PhysRevB.94.155138 ↗
34. Kushnirenko, Y. et al. Three-dimensional superconducting gap in FeSe from angle-resolved photoemission spectroscopy. Phys. Rev. B 97, 180501(R) (2018).10.1103/PhysRevB.97.180501 ↗
35. Liu, D. et al. Orbital origin of extremely anisotropic superconducting gap in nematic phase of FeSe superconductor. Phys. Rev. X 8, 031033 (2018).
36. Wang, Z. et al. Topological edge states in a high-temperature superconductor FeSe/SrTiO3 (001) film. Nat. Mater. 15, 968–973 (2016).10.1038/nmat4686 ↗
37. Yi, M. et al. Nematic energy scale and the missing electron pocket in FeSe. Phys. Rev. X 9, 041049 (2019).
38. Huh, S. et al. Absence of Y-pocket in 1-Fe Brillouin zone and reversed orbital occupation imbalance in FeSe. Commun. Phys. 3, 52 (2020).10.1038/s42005-020-0319-1 ↗
39. Su, Y., Liao, H. & Li, T. The form and origin of orbital ordering in the electronic nematic phase of iron-based superconductors. J. Phys. Condens. Matter 27, 105702 (2015).10.1088/0953-8984/27/10/105702 ↗
40. Onari, S., Yamakawa, Y. & Kontani, H. Sign-reversing orbital polarization in the nematic phase of FeSe due to the C2 symmetry breaking in the self-energy. Phys. Rev. Lett. 116, 227001 (2016).10.1103/PhysRevLett.116.227001 ↗
41. Xing, R.-Q., Classen, L. & Chubukov, A. V. Orbital order in FeSe: the case for vertex renormalization. Phys. Rev. B 98, 041108(R) (2018).10.1103/PhysRevB.98.041108 ↗
42. Yi, M., Zhang, Y., Shen, Z.-X. & Lu, D. Role of the orbital degree of freedom in iron-based superconductors. npj Quant. Mater. 2, 57 (2017).10.1038/s41535-017-0059-y ↗
43. Sprau, P. O. et al. Discovery of orbital-selective Cooper pairing in FeSe. Science 357, 75–80 (2017).10.1126/science.aal1575 ↗
44. Kostin, A. et al. Imaging orbital-selective quasiparticles in the Hund’s metal state of FeSe. Nat. Mater. 17, 869–874 (2018).10.1038/s41563-018-0151-0 ↗
45. Glasbrenner, J. et al. Effect of magnetic frustration on nematicity and superconductivity in iron chalcogenides. Nat. Phys. 11, 953–958 (2015).10.1038/nphys3434 ↗
46. Liu, K., Lu, Z.-Y. & Xiang, T. Nematic antiferromagnetic states in bulk FeSe. Phys. Rev. B 93, 205154 (2016).10.1103/PhysRevB.93.205154 ↗
47. Wang, F., Kivelson, S. A. & Lee, D.-H. Nematicity and quantum paramagnetism in FeSe. Nat. Phys. 11, 959–963 (2015).10.1038/nphys3456 ↗
48. Cococcioni, M. & De Gironcoli, S. Linear response approach to the calculation of the effective interaction parameters in the LDA+U method. Phys. Rev. B 71, 035105 (2005).10.1103/PhysRevB.71.035105 ↗
49. Meredig, B., Thompson, A., Hansen, H. A., Wolverton, C. & van de Walle, A. Method for locating low-energy solutions within DFT+U. Phys. Rev. B 82, 195128 (2010).10.1103/PhysRevB.82.195128 ↗
50. Amadon, B., Jollet, F. & Torrent, M. γ and β cerium: LDA+U calculations of ground-state parameters. Phys. Rev. B 77, 155104 (2008).10.1103/PhysRevB.77.155104 ↗
51. Cvetkovic, V. & Vafek, O. Space group symmetry, spin-orbit coupling, and the low-energy effective hamiltonian for iron-based superconductors. Phys. Rev. B 88, 134510 (2013).10.1103/PhysRevB.88.134510 ↗
52. Li, J. et al. Spin-orbital-intertwined nematic state in FeSe. Phys. Rev. X 10, 011034 (2020).
53. Zhao, L. et al. A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy. Nat. Phys. 13, 250–254 (2017).10.1038/nphys3962 ↗
54. Harter, J., Chu, H., Jiang, S., Ni, N. & Hsieh, D. Nonlinear and time-resolved optical study of the 112-type iron-based superconductor parent Ca1−xLaxFeAs2 across its structural phase transition. Phys. Rev. B 93, 104506 (2016).10.1103/PhysRevB.93.104506 ↗
55. Kityk, I., Viennois, R. & Plucinski, K. Phase transition diagnostic in iron telluride by nonlinear optical experiments. Acta Phys. Pol. A 121, 932–935 (2012).10.12693/APhysPolA.121.932 ↗
56. Li, C. et al. Evidence for an additional symmetry breaking from direct observation of band splitting in the nematic state of FeSe superconductor. https://journals.aps.org/prx/accepted/ae073K31C6016107a4ba31f563009819a004318b2 (2019).
57. Kotliar, G. et al. Electronic structure calculations with dynamical mean-field theory. Rev. Mod. Phys. 78, 865–951 (2006).10.1103/RevModPhys.78.865 ↗
58. Hedin, L. On correlation effects in electron spectroscopies and the GW approximation. J. Phys. Condens. Matter 11, R489–R528 (1999).10.1088/0953-8984/11/42/201 ↗
59. Kresse, G. & Furthmüller, J. Efficient iterative schemes for abinitio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).10.1103/PhysRevB.54.11169 ↗
60. McQueen, T. M. et al. Extreme sensitivity of superconductivity to stoichiometry in Fe1+δSe. Phys. Rev. B 79, 014522 (2009).10.1103/PhysRevB.79.014522 ↗
61. Heyd, J., Scuseria, G. E. & Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207–8215 (2003).10.1063/1.1564060 ↗
62. Heyd, J., Scuseria, G. E. & Ernzerhof, M. Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)]. J. Chem. Phys. 124, 219906 (2006).10.1063/1.2204597 ↗
63. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).10.1103/PhysRevB.50.17953 ↗
64. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976).10.1103/PhysRevB.13.5188 ↗
65. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).10.1103/PhysRevLett.77.3865 ↗
66. Dudarev, S., Botton, G., Savrasov, S., Humphreys, C. & Sutton, A. Electron-energy-loss spectra and the structural stability of nickel oxide: an LSDA+U study. Phys. Rev. B 57, 1505–1509 (1998).10.1103/PhysRevB.57.1505 ↗
67. Liechtenstein, A., Anisimov, V. & Zaanen, J. Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators. Phys. Rev. B 52, R5467–R5470 (1995).10.1103/PhysRevB.52.R5467 ↗
68. Gonze, X. et al. The ABINIT project: Impact, environment and recent developments. Comput. Phys. Commun. 248, 107042 (2020).10.1016/j.cpc.2019.107042 ↗
69. Torrent, M., Jollet, F., Bottin, F., Zérah, G. & Gonze, X. Implementation of the projector augmented-wave method in the ABINIT code: application to the study of iron under pressure. Comput. Mater. Sci. 42, 337–351 (2008).10.1016/j.commatsci.2007.07.020 ↗
70. Payne, M. C., Teter, M. P., Allan, D. C., Arias, T. & Joannopoulos, aJ. Iterative minimization techniques for abinitio total-energy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys. 64, 1045–1097 (1992).10.1103/RevModPhys.64.1045 ↗
71. Wang, Q. et al. Magnetic ground state of FeSe. Nat. Commun. 7, 12182 (2016).