- Open Access
Understanding nematicity and band structure of FeSe by first-principles study and tight-binding model
Phys. Rev. Research 8, 013298 – Published 18 March, 2026
DOI: https://doi.org/10.1103/tjzc-cbhr
Abstract
We systematically investigate the effects of spin order and orbital polarization on the electronic and magnetic structures of nematic FeSe using the method. While our calculations with on-site Coulomb repulsion can account for both the nonmagnetic state at ambient pressure and the phase transition to a stripe antiferromagnetic state at moderate pressure as observed experimentally, neither static spin order nor static orbital polarization can describe the experimental band dispersions from angle-resolved photoemission spectroscopy (ARPES) studies, due to the underestimate of quantum fluctuations. By employing a particle swarm optimization algorithm, we construct a tight-binding model with inclusion of correlation effects through seeking appropriate renormalization factors of kinetic energies, which successfully reproduce the ARPES results at various temperatures, highlighting the importance of correlations in FeSe.
Physics Subject Headings (PhySH)
Article Text
References (87)
- Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, Iron-based layered superconductor () with , J. Am. Chem. Soc. 130, 3296 (2008).
- H. Takahashi, K. Igawa, K. Arii, Y. Kamihara, M. Hirano, and H. Hosono, Superconductivity at in an iron-based layered compound , Nature (London) 453, 376 (2008).
- X. Chen, T. Wu, G. Wu, R. Liu, H. Chen, and D. Fang, Superconductivity at in , Nature (London) 453, 761 (2008).
- L. Ding, C. He, J. K. Dong, T. Wu, R. H. Liu, X. H. Chen, and S. Y. Li, Specific heat of the iron-based high- superconductor , Phys. Rev. B 77, 180510(R) (2008).
- R. Fernandes, A. Chubukov, and J. Schmalian, What drives nematic order in iron-based superconductors? Nat. Phys. 10, 97 (2014).
- A. Chubukov and P. J. Hirschfeld, Iron-based superconductors, seven years later, Phys. Today 68(6), 46 (2015).
- K. Matsuura, Y. Mizukami, Y. Arai, Y. Sugimura, N. Maejima, A. Machida, T. Watanuki, T. Fukuda, T. Yajima, Z. Hiroi, et al., Maximizing by tuning nematicity and magnetism in superconductors, Nat. Commun. 8, 1143 (2017).
- T. Shibauchi, A. Carrington, and Y. Matsuda, A quantum critical point lying beneath the superconducting dome in iron pnictides, Annu. Rev. Condens. Matter Phys. 5, 113 (2014).
- A. I. Coldea, Electronic nematic states tuned by isoelectronic substitution in bulk , Front. Phys. 8, 594500 (2021).
- A. Kreisel, P. J. Hirschfeld, and B. M. Andersen, On the remarkable superconductivity of FeSe and its close cousins, Symmetry 12, 1402 (2020).
- T. Shibauchi, T. Hanaguri, and Y. Matsuda, Exotic superconducting states in FeSe-based materials, J. Phys. Soc. Jpn. 89, 102002 (2020).
- R. Khasanov, K. Conder, E. Pomjakushina, A. Amato, C. Baines, Z. Bukowski, J. Karpinski, S. Katrych, H.-H. Klauss, H. Luetkens, A. Shengelaya, and N. D. Zhigadlo, Evidence of nodeless superconductivity in from a muon-spin-rotation study of the in-plane magnetic penetration depth, Phys. Rev. B 78, 220510(R) (2008).
- T. M. McQueen, A. J. Williams, P. W. Stephens, J. Tao, Y. Zhu, V. Ksenofontov, F. Casper, C. Felser, and R. J. Cava, Tetragonal-to-orthorhombic structural phase transition at 90 K in the superconductor , Phys. Rev. Lett. 103, 057002 (2009).
- M. Bendele, A. Amato, K. Conder, M. Elender, H. Keller, H.-H. Klauss, H. Luetkens, E. Pomjakushina, A. Raselli, and R. Khasanov, Pressure induced static magnetic order in superconducting , Phys. Rev. Lett. 104, 087003 (2010).
- J.-H. Chu, J. G. Analytis, K. De Greve, P. L. McMahon, Z. Islam, Y. Yamamoto, and I. R. Fisher, In-plane resistivity anisotropy in an underdoped iron arsenide superconductor, Science 329, 824 (2010).
- K. Nakayama, Y. Miyata, G. N. Phan, T. Sato, Y. Tanabe, T. Urata, K. Tanigaki, and T. Takahashi, Reconstruction of band structure induced by electronic nematicity in an FeSe superconductor, Phys. Rev. Lett. 113, 237001 (2014).
- P. Zhang, T. Qian, P. Richard, X. P. Wang, H. Miao, B. Q. Lv, B. B. Fu, T. Wolf, C. Meingast, X. X. Wu, Z. Q. Wang, J. P. Hu, and H. Ding, Observation of two distinct / band splittings in FeSe, Phys. Rev. B 91, 214503 (2015).
- Y. Kubota, F. Nabeshima, K. Nakayama, H. Ohsumi, Y. Tanaka, K. Tamasaku, T. Suzuki, K. Okazaki, T. Sato, A. Maeda, and M. Yabashi, Pure nematic state in the iron-based superconductor FeSe, Phys. Rev. B 108, L100501 (2023).
- Q. Wang, Y. Shen, B. Pan, Y. Hao, M. Ma, F. Zhou, P. Steffens, K. Schmalzl, T. Forrest, M. Abdel-Hafiez, et al., Strong interplay between stripe spin fluctuations, nematicity and superconductivity in FeSe, Nat. Mater. 15, 159 (2016).
- T. Chen, Y. Chen, A. Kreisel, X. Lu, A. Schneidewind, Y. Qiu, J. Park, T. G. Perring, J. R. Stewart, H. Cao, et al., Anisotropic spin fluctuations in detwinned FeSe, Nat. Mater. 18, 709 (2019).
- X. Lu, W. Zhang, Y. Tseng, R. Liu, Z. Tao, E. Paris, P. Liu, T. Chen, V. N. Strocov, Y. Song, et al., Spin-excitation anisotropy in the nematic state of detwinned FeSe, Nat. Phys. 18, 806 (2022).
- P. Massat, D. Farina, I. Paul, S. Karlsson, P. Strobel, P. Toulemonde, M.-A. Méasson, M. Cazayous, A. Sacuto, S. Kasahara, et al., Charge-induced nematicity in FeSe, Proc. Natl. Acad. Sci. USA 113, 9177 (2016).
- S.-H. Baek, D. Efremov, J. Ok, J. Kim, J. van den Brink, and B. Büchner, Orbital-driven nematicity in FeSe, Nat. Mater. 14, 210 (2015).
- C. A. Occhialini, J. J. Sanchez, Q. Song, G. Fabbris, Y. Choi, J.-W. Kim, P. J. Ryan, and R. Comin, Spontaneous orbital polarization in the nematic phase of FeSe, Nat. Mater. 22, 985 (2023).
- R. Yu and Q. Si, Antiferroquadrupolar and Ising-nematic orders of a frustrated bilinear-biquadratic Heisenberg model and implications for the magnetism of FeSe, Phys. Rev. Lett. 115, 116401 (2015).
- T. Yamada and T. Tohyama, Multipolar nematic state of nonmagnetic FeSe based on , Phys. Rev. B 104, L161110 (2021).
- T. Shimojima, Y. Suzuki, T. Sonobe, A. Nakamura, M. Sakano, J. Omachi, K. Yoshioka, M. Kuwata-Gonokami, K. Ono, H. Kumigashira, A. E. Böhmer, F. Hardy, T. Wolf, C. Meingast, H. v. Löhneysen, H. Ikeda, and K. Ishizaka, Lifting of xz/yz orbital degeneracy at the structural transition in detwinned FeSe, Phys. Rev. B 90, 121111(R) (2014).
- Y. Suzuki, T. Shimojima, T. Sonobe, A. Nakamura, M. Sakano, H. Tsuji, J. Omachi, K. Yoshioka, M. Kuwata-Gonokami, T. Watashige, R. Kobayashi, S. Kasahara, T. Shibauchi, Y. Matsuda, Y. Yamakawa, H. Kontani, and K. Ishizaka, Momentum-dependent sign inversion of orbital order in superconducting FeSe, Phys. Rev. B 92, 205117 (2015).
- M. D. Watson, T. K. Kim, A. A. Haghighirad, N. R. Davies, A. McCollam, A. Narayanan, S. F. Blake, Y. L. Chen, S. Ghannadzadeh, A. J. Schofield, M. Hoesch, C. Meingast, T. Wolf, and A. I. Coldea, Emergence of the nematic electronic state in FeSe, Phys. Rev. B 91, 155106 (2015).
- L. Fanfarillo, J. Mansart, P. Toulemonde, H. Cercellier, P. Le Fèvre, F. Bertran, B. Valenzuela, L. Benfatto, and V. Brouet, Orbital-dependent Fermi surface shrinking as a fingerprint of nematicity in FeSe, Phys. Rev. B 94, 155138 (2016).
- M. D. Watson, T. K. Kim, L. C. Rhodes, M. Eschrig, M. Hoesch, A. A. Haghighirad, and A. I. Coldea, Evidence for unidirectional nematic bond ordering in FeSe, Phys. Rev. B 94, 201107(R) (2016).
- A. Fedorov, A. Yaresko, T. Kim, Y. Kushnirenko, E. Haubold, T. Wolf, M. Hoesch, A. Grüneis, B. Büchner, and S. Borisenko, Effect of nematic ordering on electronic structure of FeSe, Sci. Rep. 6, 36834 (2016).
- M. D. Watson, A. A. Haghighirad, H. Takita, W. Mansuer, H. Iwasawa, E. F. Schwier, A. Ino, and M. Hoesch, Shifts and splittings of the hole bands in the nematic phase of FeSe, J. Phys. Soc. Jpn. 86, 053703 (2017).
- M. D. Watson, A. A. Haghighirad, L. C. Rhodes, M. Hoesch, and T. K. Kim, Electronic anisotropies revealed by detwinned angle-resolved photo-emission spectroscopy measurements of FeSe, New J. Phys. 19, 103021 (2017).
- L. C. Rhodes, M. D. Watson, A. A. Haghighirad, M. Eschrig, and T. K. Kim, Strongly enhanced temperature dependence of the chemical potential in FeSe, Phys. Rev. B 95, 195111 (2017).
- Y. S. Kushnirenko, A. A. Kordyuk, A. V. Fedorov, E. Haubold, T. Wolf, B. Büchner, and S. V. Borisenko, Anomalous temperature evolution of the electronic structure of FeSe, Phys. Rev. B 96, 100504(R) (2017).
- D. Liu, C. Li, J. Huang, B. Lei, L. Wang, X. Wu, B. Shen, Q. Gao, Y. Zhang, X. Liu, et al., Orbital origin of extremely anisotropic superconducting gap in nematic phase of FeSe superconductor, Phys. Rev. X 8, 031033 (2018).
- L. C. Rhodes, M. D. Watson, A. A. Haghighirad, D. V. Evtushinsky, M. Eschrig, and T. K. Kim, Scaling of the superconducting gap with orbital character in FeSe, Phys. Rev. B 98, 180503(R) (2018).
- Y. S. Kushnirenko, A. V. Fedorov, E. Haubold, S. Thirupathaiah, T. Wolf, S. Aswartham, I. Morozov, T. K. Kim, B. Büchner, and S. V. Borisenko, Three-dimensional superconducting gap in FeSe from angle-resolved photoemission spectroscopy, Phys. Rev. B 97, 180501(R) (2018).
- M. Yi, H. Pfau, Y. Zhang, Y. He, H. Wu, T. Chen, Z. R. Ye, M. Hashimoto, R. Yu, Q. Si, D.-H. Lee, P. Dai, Z.-X. Shen, D. H. Lu, and R. J. Birgeneau, Nematic energy scale and the missing electron pocket in FeSe, Phys. Rev. X 9, 041049 (2019).
- H. Pfau, S. D. Chen, M. Yi, M. Hashimoto, C. R. Rotundu, J. C. Palmstrom, T. Chen, P.-C. Dai, J. Straquadine, A. Hristov, R. J. Birgeneau, I. R. Fisher, D. Lu, and Z.-X. Shen, Momentum dependence of the nematic order parameter in iron-based superconductors, Phys. Rev. Lett. 123, 066402 (2019).
- S. Huh, J. Seo, B. Kim, S. Cho, J. K. Jung, S. Kim, C. I. Kwon, J. S. Kim, Y. Koh, W. Kyung, et al., Absence of Y-pocket in 1-Fe Brillouin zone and reversed orbital occupation imbalance in FeSe, Commun. Phys. 3, 52 (2020).
- L. C. Rhodes, M. D. Watson, A. A. Haghighirad, D. V. Evtushinsky, and T. K. Kim, Revealing the single electron pocket of FeSe in a single orthorhombic domain, Phys. Rev. B 101, 235128 (2020).
- C. Cai, T. Han, Z. Wang, L. Chen, Y. Wang, Z. Xin, M. Ma, Y. Li, and Y. Zhang, Anomalous spectral weight transfer in the nematic state of iron-selenide superconductor, Chin. Phys. B 29, 077401 (2020).
- H. Pfau, M. Yi, M. Hashimoto, T. Chen, P.-C. Dai, Z.-X. Shen, S.-K. Mo, and D. Lu, Quasiparticle coherence in the nematic state of FeSe, Phys. Rev. B 104, L241101 (2021).
- Y. Yang, Q. Wang, S. Duan, H. Wo, C. Huang, S. Wang, L. Gu, D. Xiang, D. Qian, J. Zhao, and W. Zhang, Anomalous contribution to the nematic electronic states from the structural transition in FeSe revealed by time- and angle-resolved photoemission spectroscopy, Phys. Rev. Lett. 128, 246401 (2022).
- J. Glasbrenner, I. Mazin, H. O. Jeschke, P. Hirschfeld, R. Fernandes, and R. Valentí, Effect of magnetic frustration on nematicity and superconductivity in iron chalcogenides, Nat. Phys. 11, 953 (2015).
- H.-Y. Cao, S. Chen, H. Xiang, and X.-G. Gong, Antiferromagnetic ground state with pair-checkerboard order in FeSe, Phys. Rev. B 91, 020504(R) (2015).
- M. Hirayama, T. Misawa, T. Miyake, and M. Imada, Ab initio studies of magnetism in the iron chalcogenides FeTe and FeSe, J. Phys. Soc. Jpn. 84, 093703 (2015).
- S. Pokharel and H. Fu, Understanding the importance of local magnetic moment in monolayer FeSe, Phys. Rev. B 104, 195110 (2021).
- A. E. Böhmer and A. Kreisel, Nematicity, magnetism and superconductivity in FeSe, J. Phys.: Condens. Matter 30, 023001 (2018).
- J. Sun, K. Matsuura, G. Ye, Y. Mizukami, M. Shimozawa, K. Matsubayashi, M. Yamashita, T. Watashige, S. Kasahara, Y. Matsuda, et al., Dome-shaped magnetic order competing with high-temperature superconductivity at high pressures in FeSe, Nat. Commun. 7, 12146 (2016).
- A. E. Böhmer, K. Kothapalli, W. T. Jayasekara, J. M. Wilde, B. Li, A. Sapkota, B. G. Ueland, P. Das, Y. Xiao, W. Bi, J. Zhao, E. E. Alp, S. L. Bud'ko, P. C. Canfield, A. I. Goldman, and A. Kreyssig, Distinct pressure evolution of coupled nematic and magnetic orders in FeSe, Phys. Rev. B 100, 064515 (2019).
- X. Long, S. Zhang, F. Wang, and Z. Liu, A first-principle perspective on electronic nematicity in FeSe, npj Quantum Mater. 5, 50 (2020).
- L. C. Rhodes, M. Eschrig, T. K. Kim, and M. D. Watson, FeSe and the missing electron pocket problem, Front. Phys. 10, 859017 (2022).
- S. Rößler, M. Coduri, A. A. Tsirlin, C. Ritter, G. Cuello, C. Koz, L. Muzica, U. Schwarz, U. K. Rößler, S. Wirth, and M. Scavini, Nematic state of the FeSe superconductor, Phys. Rev. B 105, 064505 (2022).
- C.-C. Lee, W.-G. Yin, and W. Ku, Ferro-orbital order and strong magnetic anisotropy in the parent compounds of iron-pnictide superconductors, Phys. Rev. Lett. 103, 267001 (2009).
- R. M. Fernandes and O. Vafek, Distinguishing spin-orbit coupling and nematic order in the electronic spectrum of iron-based superconductors, Phys. Rev. B 90, 214514 (2014).
- L. C. Rhodes, J. Böker, M. A. Müller, M. Eschrig, and I. M. Eremin, Non-local nematicity and the missing electron pocket in FeSe, npj Quantum Mater. 6, 45 (2021).
- D. Steffensen, A. Kreisel, P. J. Hirschfeld, and B. M. Andersen, Interorbital nematicity and the origin of a single electron Fermi pocket in FeSe, Phys. Rev. B 103, 054505 (2021).
- H. Eschrig and K. Koepernik, Tight-binding models for the iron-based superconductors, Phys. Rev. B 80, 104503 (2009).
- P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka, J. Luitz, R. Laskowski, F. Tran, and L. D. Marks, WIEN2k: An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Karlheinz Schwarz, Vienna University of Technology, Austria, 2018).
- J. P. Perdew and A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B 23, 5048 (1981).
- M. T. Czyżyk and G. A. Sawatzky, Local-density functional and on-site correlations: The electronic structure of and , Phys. Rev. B 49, 14211 (1994).
- E. R. Ylvisaker, W. E. Pickett, and K. Koepernik, Anisotropy and magnetism in the method, Phys. Rev. B 79, 035103 (2009).
- Z.-Y. Song, X.-C. Jiang, X.-F. Ouyang, and Y.-Z. Zhang, Breakdown of Hund's rule for CuFeAs, Phys. Rev. B 103, 125123 (2021).
- T. Miyake, K. Nakamura, R. Arita, and M. Imada, Comparison of ab initio low-energy models for LaFePO, LaFeAsO, , LiFeAs, FeSe, and FeTe: Electron correlation and covalency, J. Phys. Soc. Jpn. 79, 044705 (2010).
- Q. Wang, Y. Shen, B. Pan, X. Zhang, K. Ikeuchi, K. Iida, A. Christianson, H. Walker, D. Adroja, M. Abdel-Hafiez, et al., Magnetic ground state of FeSe, Nat. Commun. 7, 12182 (2016).
- S. Margadonna, Y. Takabayashi, Y. Ohishi, Y. Mizuguchi, Y. Takano, T. Kagayama, T. Nakagawa, M. Takata, and K. Prassides, Pressure evolution of the low-temperature crystal structure and bonding of the superconductor FeSe , Phys. Rev. B 80, 064506 (2009).
- J. Kuneš, R. Arita, P. Wissgott, A. Toschi, H. Ikeda, and K. Held, Wien2Wannier: From linearized augmented plane waves to maximally localized Wannier functions, Comput. Phys. Commun. 181, 1888 (2010).
- A. A. Mostofi, J. R. Yates, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, Wannier90: A tool for obtaining maximally-localised Wannier functions, Comput. Phys. Commun. 178, 685 (2008).
- J. Kennedy and R. Eberhart, Particle swarm optimization, in Proceedings of ICNN’95—International Conference on Neural Networks (IEEE, New York, NY, 1995), Vol. 4, pp. 1942–1948.
- M. Yi, Y. Zhang, Z.-X. Shen, and D. Lu, Role of the orbital degree of freedom in iron-based superconductors, npj Quantum Mater. 2, 57 (2017).
- W. Z. Kunliang Bu, Observation of an electronic order along [110] direction in FeSe, Nat. Commun. 12, 1385 (2021).
- V. Cvetkovic and O. Vafek, Space group symmetry, spin-orbit coupling, and the low-energy effective Hamiltonian for iron-based superconductors, Phys. Rev. B 88, 134510 (2013).
- T. Saito, Y. Yamakawa, S. Onari, and H. Kontani, Revisiting orbital-fluctuation-mediated superconductivity in LiFeAs: Nontrivial spin-orbit interaction effects on the band structure and superconducting gap function, Phys. Rev. B 92, 134522 (2015).
- V. Brouet, M. F. Jensen, P.-H. Lin, A. Taleb-Ibrahimi, P. Le Fèvre, F. Bertran, C.-H. Lin, W. Ku, A. Forget, and D. Colson, Impact of the two Fe unit cell on the electronic structure measured by ARPES in iron pnictides, Phys. Rev. B 86, 075123 (2012).
- I. Leonov, S. L. Skornyakov, V. I. Anisimov, and D. Vollhardt, Correlation-driven topological Fermi surface transition in FeSe, Phys. Rev. Lett. 115, 106402 (2015).
- M. D. Watson, S. Backes, A. A. Haghighirad, M. Hoesch, T. K. Kim, A. I. Coldea, and R. Valentí, Formation of Hubbard-like bands as a fingerprint of strong electron-electron interactions in FeSe, Phys. Rev. B 95, 081106(R) (2017).
- M. Aichhorn, S. Biermann, T. Miyake, A. Georges, and M. Imada, Theoretical evidence for strong correlations and incoherent metallic state in FeSe, Phys. Rev. B 82, 064504 (2010).
- S. Mukherjee, A. Kreisel, P. J. Hirschfeld, and B. M. Andersen, Model of electronic structure and superconductivity in orbitally ordered FeSe, Phys. Rev. Lett. 115, 026402 (2015).
- Y. Yamakawa, S. Onari, and H. Kontani, Nematicity and magnetism in FeSe and other families of Fe-based superconductors, Phys. Rev. X 6, 021032 (2016).
- P. O. Sprau, A. Kostin, A. Kreisel, A. E. Böhmer, V. Taufour, P. C. Canfield, S. Mukherjee, P. J. Hirschfeld, B. M. Andersen, and J. S. Davis, Discovery of orbital-selective cooper pairing in FeSe, Science 357, 75 (2017).
- A. Kreisel, B. M. Andersen, P. O. Sprau, A. Kostin, J. C. Seamus Davis, and P. J. Hirschfeld, Orbital selective pairing and gap structures of iron-based superconductors, Phys. Rev. B 95, 174504 (2017).
- J. Li, B. Lei, D. Zhao, L. P. Nie, D. W. Song, L. X. Zheng, S. J. Li, B. L. Kang, X. G. Luo, T. Wu, and X. H. Chen, Spin-orbital-intertwined nematic state in FeSe, Phys. Rev. X 10, 011034 (2020).
- K. Jiang, J. Hu, H. Ding, and Z. Wang, Interatomic Coulomb interaction and electron nematic bond order in FeSe, Phys. Rev. B 93, 115138 (2016).
- S. Moser, An experimentalist's guide to the matrix element in angle resolved photoemission, J. Electron Spectrosc. Relat. Phenom. 214, 29 (2017).