Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Prediction of pseudogap formation due to d-wave bond-order in organic superconductor κ−(BEDT-TTF)2X

Rina Tazai1, Youichi Yamakawa1, Masahisa Tsuchiizu2, and Hiroshi Kontani1

  • 1Department of Physics, Nagoya University, Furo-cho, Nagoya 464-8602, Japan
  • 2Department of Physics, Nara Women's University, Nara 630-8506, Japan

Phys. Rev. Research 3, L022014 – Published 19 May, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L022014

Abstract

Rich hidden unconventional orders with pseudogap formation, such as the intersite bond order (BO), attract increasing attention in condensed matter physics. Here, we investigate the hidden order formation in organic unconventional superconductor κ−(BEDT-TTF)2X. We predict the formation of d-wave BO at wavelength q=QB=(δ,δ) (δ=0.38π) for the first time, based on both the functional renormalization group (fRG) and the density-wave equation theories. The origin of the BO is the quantum interference among antiferromagnetic spin fluctuations. This prediction leads to distinct pseudogap-like reduction in the NMR 1/T1 relaxation rate and in the density-of-states, consistently with essential experimental reports. The present theory would be applicable for other strongly correlated metals with pseudogap formation.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (63)

  1. K. Kanoda, Electron correlation, metal-insulator transition and superconductivity in quasi-2D organic systems, (ET)2X, Physica C 282-287, 299 (1997).
  2. K. Kanoda and R. Kato, Mott physics in organic conductors with triangular lattices, Annu. Rev. Condens. Matter Phys. 2, 167 (2011).
  3. Y. Shimizu, K. Miyagawa, K. Kanoda, M. Maesato, and G. Saito, Spin Liquid State in an Organic Mott Insulator with a Triangular Lattice, Phys. Rev. Lett. 91, 107001 (2003).
  4. J. Schmalian, Pairing due to Spin Fluctuations in Layered Organic Superconductors, Phys. Rev. Lett. 81, 4232 (1998).
  5. H. Kino and H. Kontani, Phase diagram of superconductivity on the anisotropic triangular lattice Hubbard model: An effective model of κ-(BEDT-TTF) salts, J. Phys. Soc. Jpn. 67, 3691 (1998).
  6. H. Kondo and T. Moriya, Spin fluctuation-induced superconductivity in organic compounds, J. Phys. Soc. Jpn. 67, 3695 (1998).
  7. H. Kontani and H. Kino, Theory of the Hall coefficient and resistivity for the layered organic superconductors κ−(BEDT-TTF)2X, Phys. Rev. B 63, 134524 (2001).
  8. K. Kuroki, Pairing symmetry competition in organic superconductors, J. Phys. Soc. Jpn. 75, 051013 (2006).
  9. H. Watanabe, H. Seo, and S. Yunoki, Mechanism of superconductivity and electron-hole doping asymmetry in κ-type molecular conductors, Nat. Commun. 10, 3167 (2019).
  10. B. Kyung and A.-M. S. Tremblay, Mott Transition, Antiferromagnetism, and d-Wave Superconductivity in Two-Dimensional Organic Conductors, Phys. Rev. Lett. 97, 046402 (2006).
  11. T. Arai, K. Ichimura, K. Nomura, S. Takasaki, J. Yamada, S. Nakatsuji, and H. Anzai, Superconducting and normal-state gaps in κ−(BEDT-TTF)2Cu(NCS)2 studied by STM spectroscopy, Solid State Commun. 116, 679 (2000).
  12. T. Kobayashi, Y. Ihara, Y. Saito, and A. Kawamoto, Microscopic observation of superconducting fluctuations in κ−(BEDT-TTF)2Cu[N(CN)2]Br by C13 NMR spectroscopy, Phys. Rev. B 89, 165141 (2014).
  13. Y. Eto, M. Itaya, and A. Kawamoto, Non-Fermi-liquid behavior of the organic superconductor κ−(BEDT-TTF)4Hg2.89Br8 probed by C13 NMR, Phys. Rev. B 81, 212503 (2010).
  14. S. Tsuchiya, K. Nakagawa, J. Yamada, H. Taniguchi, and Y. Toda, Photoinduced phase separation with local structural ordering in organic molecular conductors, Phys. Rev. B 96, 134311 (2017).
  15. K. Nakagawa, S. Tsuchiya, J. Yamada, and Y. Toda, Fluctuating superconductivity in κ-type organic compounds probed by polarized time-resolved spectroscopy, Europhys. Lett. 122, 67003 (2018).
  16. H. Kontani, Anomalous transport phenomena in Fermi liquids with strong magnetic fluctuations, Rep. Prog. Phys. 71, 026501 (2008).
  17. Y. Yanase T. Jujo, T. Nomura, H. Ikeda, T. Hotta, and K. Yamada, Theory of superconductivity in strongly correlated electron systems, Phys. Rep. 387, 1 (2003).
  18. T. Moriya and K. Ueda, Spin fluctuations and high temperature superconductivity, Adv. Phys. 49, 555 (2000).
  19. J. Schmalian, D. Pines, and B. Stojkovic, Weak Pseudogap Behavior in the Underdoped Cuprate Superconductors, Phys. Rev. Lett. 80, 3839 (1998)
  20. B. Kyung, V. Hankevych, A. M. Dare, and A. M. S. Tremblay, Pseudogap and Spin Fluctuations in the Normal State of the Electron-Doped Cuprates, Phys. Rev. Lett. 93, 147004 (2004).
  21. F. Kagawa, K. Miyagawa, and K. Kanoda, Unconventional critical behaviour in a quasi-two-dimensional organic conductor, Nature (London) 436, 534 (2005).
  22. J. Kang, S.-L. Yu, T. Xiang, and J.-X. Li, Pseudogap and Fermi arc in κ-type organic superconductors, Phys. Rev. B 84, 064520 (2011).
  23. M. Revelli Beaumont, P. Hemme, Y. Gallais, A. Sacuto, K. Jacob, L. Valade, D. de Caro, C. Faulmann, and M. Cazayous, Possible observation of the signature of the bad metal phase and its crossover to a Fermi liquid in κ−(BEDT-TTF)2Cu(NCS)2 bulk and nanoparticles by Raman scattering, J. Phys.: Condens. Matter 33, 125403 (2021).
  24. G. Ghiringhelli, M. L. Tacon, M. Minola, S. Blanco-Canosa, C. Mazzoli, N. B. Brookes, G. M. D. Luca, A. Frano, D. G. Hawthorn, F. He, T. Loew, M. M. Sala, D. C. Peets, M. Salluzzo, E. Schierle, R. Sutarto, G. A. Sawatzky, E. Weschke, B. Keimer, and L. Braicovich, Long-range incommensurate charge fluctuations in (Y, Nd)Ba2Cu3O6+x, Science 337, 821 (2012).
  25. R. Comin, A. Frano, M. M. Yee, Y. Yoshida, H. Eisaki, E. Schierle, E. Weschke, . Sutarto, F. He, A. Soumyanarayanan, Y. He, M. L. Tacon, I. S. Elfimov, J. E. Hffman, G. A. Sawatzky, B. Keimer, and A. Damascelli, Charge order driven by Fermi-arc instability in Bi2Sr2−xLaxCuO+δ, Science 343, 390 (2014).
  26. Y. Kohsaka, T. Hanaguri, M. Azuma, M. Takano, J. C. Davis, and H. Takagi, Visualization of the emergence of the pseudogap state and the evolution to superconductivity in a lightly hole-doped Mott insulator, Nat. Phys. 8, 534 (2012).
  27. K. Fujita, M. H. Hamidian, S. D. Edkins, C. K. Kim, Y. Kohsaka, M. Azuma, M. Takano, H. Takagi, H. Eisaki, S. Uchida, A. Allais, M. J. Lawler, E.-A. Kim, S. Sachdev, and J. C. S. Davis, Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates, Proc. Natl. Acad. Sci. U.S.A. 111, E3026 (2014).
  28. T. Wu, H. Mayaffre, S. Krämer, M. Horvatić, C. Berthier, P. L. Kuhns, A. P. Reyes, R. Liang, W. N. Hardy, D. A. Bonn, and M.-H. Julien, Emergence of charge order from the vortex state of a high-temperature superconductor, Nat. Commun. 4, 2113 (2013).
  29. T. Wu, H. Mayaffre, S. Krämer, M. Horvatić, C. Berthier, W. N. Hardy, R. Liang, D. A. Bonn, and M.-H. Julien, Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy, Nat. Commun. 6, 6438 (2015).
  30. Y. Sato, S. Kasahara, H. Murayama, Y. Kasahara, E.-G. Moon, T. Nishizaki, T. Loew, J. Porras, B. Keimer, T. Shibauchi, and Y. Matsuda, Thermodynamic evidence for a nematic phase transition at the onset of the pseudogap in YBa2Cu3Oy, Nat. Phys. 13, 1074 (2017).
  31. H. Murayama, Y. Sato, R. Kurihara, S. Kasahara, Y. Mizukami, Y. Kasahara, H. Uchiyama, A. Yamamoto, E.-G. Moon, J. Cai, J. Freyermuth, M. Greven, T. Shibauchi, and Y. Matsuda, Diagonal nematicity in the pseudogap phase of HgBa2CuO4+δ, Nat. Commun. 10, 3282 (2019).
  32. S. Nakata, M. Horio, K. Koshiishi, K. Hagiwara, C. Lin, M. Suzuki, S. Ideta, K. Tanaka, D. Song, Y. Yoshida, H. Eisaki, and A. Fujimori, Nematicity in the pseudogap state of cuprate superconductors revealed by angle-resolved photoemission spectroscopy, arXiv:1811.10028.
  33. K. Ishida, S. Hosoi, Y. Teramoto, T. Usui, Y. Mizukami, K. Itaka, Y. Matsuda, T. Watanabe, and T. Shibauchi, Divergent nematic susceptibility near the pseudogap critical point in a cuprate superconductor, J. Phys. Soc. Jpn. 89, 064707 (2020).
  34. W. Wang, J. Luo, C. G. Wang, J. Yang, Y. Kodama, R. Zhou, and G.-Q. Zheng, Microscopic evidence for the intra-unit-cell electronic nematicity inside the pseudogap phase in YBa2Cu4O8, Sci. China Phys. Mech. Astron. 64, 237413 (2021).
  35. C. M. Varma, Non-Fermi-liquid states and pairing instability of a general model of copper oxide metals, Phys. Rev. B 55, 14554 (1997).
  36. H. Yokoyama, S. Tamura, and M. Ogata, Staggered flux state in two-dimensional hubbard models, J. Phys. Soc. Jpn. 85, 124707 (2016).
  37. H. Kontani, Y. Yamakawa, R. Tazai, and S. Onari, Odd-parity spin-loop-current order mediated by transverse spin fluctuations in cuprates and related electron systems, Phys. Rev. Research 3, 013127 (2021).
  38. S. Bulut, W. A. Atkinson, and A. P. Kampf, Spatially modulated electronic nematicity in the three-band model of cuprate superconductors, Phys. Rev. B 88, 155132 (2013).
  39. Y. Wang and A. V. Chubukov, Charge-density-wave order with momentum (2Q,0) and (0,2Q) within the spin-fermion model: Continuous and discrete symmetry breaking, preemptive composite order, and relation to pseudogap in hole-doped cuprates, Phys. Rev. B 90, 035149 (2014).
  40. R.-Q. Xing, L. Classen, and A. V. Chubukov, Orbital order in FeSe: The case for vertex renormalization, Phys. Rev. B 98, 041108(R) (2018).
  41. T. Holder and W. Metzner, Incommensurate nematic fluctuations in two-dimensional metals, Phys. Rev. B 85, 165130 (2012).
  42. M. A. Metlitski and S. Sachdev, Instabilities near the onset of spin density wave order in metals, New J. Phys. 12, 105007 (2010); S. Sachdev and R. La Placa, Bond Order in Two-Dimensional Metals with Antiferromagnetic Exchange Interactions, Phys. Rev. Lett. 111, 027202 (2013).
  43. J. C. S. Davis and D.-H. Lee, Concepts relating magnetic interactions, intertwined electronic orders, and strongly correlated superconductivity, Proc. Natl. Acad. Sci. U.S.A. 110, 17623 (2013).
  44. E. Berg, E. Fradkin, S. A. Kivelson, and J. M. Tranquada, Striped superconductors: How spin, charge and superconducting orders intertwine in the cuprates, New J. Phys. 11, 115004 (2009).
  45. Y. Yamakawa, and H. Kontani, Spin-Fluctuation-Driven Nematic Charge-Density Wave in Cuprate Superconductors: Impact of Aslamazov-Larkin Vertex Corrections, Phys. Rev. Lett. 114, 257001 (2015).
  46. M. Tsuchiizu, Y. Yamakawa, and H. Kontani, p-orbital density wave with d symmetry in high-Tc cuprate superconductors predicted by renormalization-group + constrained RPA theory, Phys. Rev. B 93, 155148 (2016).
  47. M. Tsuchiizu, K. Kawaguchi, Y. Yamakawa, and H. Kontani, Multistage electronic nematic transitions in cuprate superconductors: A functional-renormalization-group analysis, Phys. Rev. B 97, 165131 (2018).
  48. K. Kawaguchi, Y. Yamakawa, M. Tsuchiizu, and H. Kontani, Competing unconventional charge-density-wave states in cuprate superconductors: Spin-fluctuation-driven mechanism, J. Phys. Soc. Jpn. 86, 063707 (2017).
  49. S. Onari and H. Kontani, Self-consistent Vertex Correction Analysis for Iron-based Superconductors: Mechanism of Coulomb Interaction-Driven Orbital Fluctuations, Phys. Rev. Lett. 109, 137001 (2012).
  50. 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).
  51. S. Onari, Y. Yamakawa, and H. Kontani, 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).
  52. S. Onari and H. Kontani, Origin of diverse nematic orders in Fe-based superconductors: 45 degree rotated nematicity in AFe2As2 (A=Sc, Rb), Phys. Rev. B 100, 020507(R) (2019).
  53. S. Onari and H. Kontani, Hidden antiferronematic order in Fe-based superconductor BaFe2As2 and NaFeAs above TS, Phys. Rev. Research 2, 042005(R) (2020).
  54. R. Tazai and H. Kontani, Multipole fluctuation theory for heavy fermion systems: Application to multipole orders in CeB6, Phys. Rev. B 100, 241103(R) (2019).
  55. W. Metzner, M. Salmhofer, C. Honerkamp, V. Meden, and K. Schönhammer, Functional renormalization group approach to correlated fermion systems, Rev. Mod. Phys. 84, 299 (2012).
  56. C. Honerkamp, Charge instabilities at the metamagnetic transition of itinerant electron systems, Phys. Rev. B 72, 115103 (2005).
  57. C. Husemann and W. Metzner, Incommensurate nematic fluctuations in the two-dimensional Hubbard model, Phys. Rev. B 86, 085113 (2012).
  58. M. Tsuchiizu, Y. Ohno, S. Onari, and H. Kontani, Orbital Nematic Instability in the Two-Orbital Hubbard Model: Renormalization-Group + Constrained RPA Analysis, Phys. Rev. Lett. 111, 057003 (2013).
  59. R. Tazai, Y. Yamakawa, M. Tsuchiizu, and H. Kontani, Functional renormalization group study of orbital fluctuation mediated superconductivity: Impact of the electron-boson coupling vertex corrections, Phys. Rev. B 94, 115155 (2016).
  60. H. Kino and H. Fukuyama, Phase diagram of two-dimensional organic conductors: (BEDT-TTF)2X, and references therein, J. Phys. Soc. Jpn. 65, 2158 (1996).
  61. B. J. Powell and R. H. McKenzie, Quantum frustration in organic Mott insulators: From spin liquids to unconventional superconductors, Rep. Prog. Phys. 74, 056501 (2011).
  62. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L022014 for additional explanation for RG+cRPA method, and additional numerical results for t′/t=0.7 in κ−(BEDT-TTF)2X model are presented.
  63. W. Ku, T. Berlijn, and C.-C. Lee, Unfolding First-Principles Band Structures, Phys. Rev. Lett. 104, 216401 (2010).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation