J. Phys. Soc. Jpn. 90, 111006 (2021) [8 Pages]
SPECIAL TOPICS: Charge Orders and Fluctuations in Cuprate High-temperature Superconductors

In-plane Isotropy of the Low Energy Phonon Anomalies in YBa2Cu3O6+x

+ Affiliations
1Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany2Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany3Japan Synchrotron Radiation Research Institute (JASRI/SPring-8), Sayo, Hyogo 679-5198, Japan

We study the temperature dependence of the low energy phonons in the \((H,0,L)\) reciprocal plane of the highly ordered ortho-II YBa2Cu3O6.55 cuprate high temperature superconductor by means of high-resolution inelastic x-ray scattering. Anomalies associated with the emergence of long-range charge density wave (CDW) fluctuations are observed, and are qualitatively similar to those previously observed in the \((0,K,L)\) plane. This confirms the unconventional nature of this bi-dimensional CDW, which is not soft-phonon driven. With the support of first principles calculations, the symmetry of the anomalous phonon is identified and is found to match that of the charge modulation. This suggests in turn that these anomalies originate from a direct coupling between the phonons and the collective CDW excitations.

©2021 The Physical Society of Japan


  • 1 A. Frano, S. Blanco-Canosa, B. Keimer, and R. J. Birgeneau, J. Phys.: Condens. Matter 32, 374005 (2020). 10.1088/1361-648X/ab6140 CrossrefGoogle Scholar
  • 2 B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Zaanen, Nature 518, 179 (2015). 10.1038/nature14165 CrossrefGoogle Scholar
  • 3 L. Pintschovius, W. Reichardt, M. Kläser, T. Wolf, and H. v. Löhneysen, Phys. Rev. Lett. 89, 037001 (2002). 10.1103/PhysRevLett.89.037001 CrossrefGoogle Scholar
  • 4 D. Reznik, L. Pintschovius, M. Ito, S. Iikubo, M. Sato, H. Goka, M. Fujita, K. Yamada, G. D. Gu, and J. M. Tranquada, Nature 440, 1170 (2006). 10.1038/nature04704 CrossrefGoogle Scholar
  • 5 M. Raichle, D. Reznik, D. Lamago, R. Heid, Y. Li, M. Bakr, C. Ulrich, V. Hinkov, K. Hradil, C. T. Lin, and B. Keimer, Phys. Rev. Lett. 107, 177004 (2011). 10.1103/PhysRevLett.107.177004 CrossrefGoogle Scholar
  • 6 D. Reznik, Physica C 481, 75 (2012). 10.1016/j.physc.2012.01.024 CrossrefGoogle Scholar
  • 7 E. Blackburn, J. Chang, A. H. Said, B. M. Leu, Ruixing Liang, D. A. Bonn, W. N. Hardy, E. M. Forgan, and S. M. Hayden, Phys. Rev. B 88, 054506 (2013). 10.1103/PhysRevB.88.054506 CrossrefGoogle Scholar
  • 8 M. Le Tacon, A. Bosak, S. M. Souliou, G. Dellea, T. Loew, R. Heid, K-P. Bohnen, G. Ghiringhelli, M. Krisch, and B. Keimer, Nat. Phys. 10, 52 (2014). 10.1038/nphys2805 CrossrefGoogle Scholar
  • 9 H. Miao, D. Ishikawa, R. Heid, M. Le Tacon, G. Fabbris, D. Meyers, G. D. Gu, A. Q. R. Baron, and M. P. M. Dean, Phys. Rev. X 8, 011008 (2018). 10.1103/PhysRevX.8.011008 CrossrefGoogle Scholar
  • 10 B. Renker, L. Pintschovius, W. Gläser, H. Rietschel, R. Comès, L. Liebert, and W. Drexel, Phys. Rev. Lett. 32, 836 (1974). 10.1103/PhysRevLett.32.836 CrossrefGoogle Scholar
  • 11 M. Hoesch, A. Bosak, D. Chernyshov, H. Berger, and M. Krisch, Phys. Rev. Lett. 102, 086402 (2009). 10.1103/PhysRevLett.102.086402 CrossrefGoogle Scholar
  • 12 M. D. Johannes, I. I. Mazin, and C. A. Howells, Phys. Rev. B 73, 205102 (2006). 10.1103/PhysRevB.73.205102 CrossrefGoogle Scholar
  • 13 S. M. Souliou, H. Gretarsson, G. Garbarino, A. Bosak, J. Porras, T. Loew, B. Keimer, and M. Le Tacon, Phys. Rev. B 97, 020503 (2018). 10.1103/PhysRevB.97.020503 CrossrefGoogle Scholar
  • 14 J. Chang, E. Blackburn, A. T. Holmes, N. B. Christensen, J. Larsen, J. Mesot, Ruixing Liang, D. A. Bonn, W. N. Hardy, A. Watenphul, M. v. Zimmermann, E. M. Forgan, and S. M. Hayden, Nat. Phys. 8, 871 (2012). 10.1038/nphys2456 CrossrefGoogle Scholar
  • 15 E. Blackburn, J. Chang, M. Hücker, A. T. Holmes, N. B. Christensen, Ruixing Liang, D. A. Bonn, W. N. Hardy, U. Rütt, O. Gutowski, M. v. Zimmermann, E. M. Forgan, and S. M. Hayden, Phys. Rev. Lett. 110, 137004 (2013). 10.1103/PhysRevLett.110.137004 CrossrefGoogle Scholar
  • 16 S. Blanco-Canosa, A. Frano, E. Schierle, J. Porras, T. Loew, M. Minola, M. Bluschke, E. Weschke, B. Keimer, and M. Le Tacon, Phys. Rev. B 90, 054513 (2014). 10.1103/PhysRevB.90.054513 CrossrefGoogle Scholar
  • 17 M. Hücker, N. B. Christensen, A. T. Holmes, E. Blackburn, E. M. Forgan, Ruixing Liang, D. A. Bonn, W. N. Hardy, O. Gutowski, M. v. Zimmermann, S. M. Hayden, and J. Chang, Phys. Rev. B 90, 054514 (2014). 10.1103/PhysRevB.90.054514 CrossrefGoogle Scholar
  • 18 I. Vinograd, R. Zhou, H. Mayaffre, S. Krämer, R. Liang, W. N. Hardy, D. A. Bonn, and M.-H. Julien, Phys. Rev. B 100, 094502 (2019). 10.1103/PhysRevB.100.094502 CrossrefGoogle Scholar
  • 19 S. M. Souliou, A. Bosak, G. Garbarino, and M. Le Tacon, Supercond. Sci. Technol. 33, 124004 (2020). 10.1088/1361-6668/abbdc3 CrossrefGoogle Scholar
  • 20 H.-H. Kim, S. M. Souliou, M. E. Barber, E. Lefrançois, M. Minola, M. Tortora, R. Heid, N. Nandi, R. A. Borzi, G. Garbarino, A. Bosak, J. Porras, T. Loew, M. König, P. J. W. Moll, A. P. Mackenzie, B. Keimer, C. W. Hicks, and M. Le Tacon, Science 362, 1040 (2018). 10.1126/science.aat4708 CrossrefGoogle Scholar
  • 21 H.-H. Kim, E. Lefrançois, K. Kummer, R. Fumagalli, N. B. Brookes, D. Betto, S. Nakata, M. Tortora, J. Porras, T. Loew, M. E. Barber, L. Braicovich, A. P. Mackenzie, C. W. Hicks, B. Keimer, M. Minola, and M. Le Tacon, Phys. Rev. Lett. 126, 037002 (2021). 10.1103/PhysRevLett.126.037002 CrossrefGoogle Scholar
  • 22 S. Gerber, H. Jang, H. Nojiri, S. Matsuzawa, H. Yasumura, D. A. Bonn, R. Liang, W. N. Hardy, Z. Islam, A. Mehta, S. Song, M. Sikorski, D. Stefanescu, Y. Feng, S. A. Kivelson, T. P. Devereaux, Z. X. Shen, C.-C. Kao, W.-S. Lee, D. Zhu, and J.-S. Lee, Science 350, 949 (2015). 10.1126/science.aac6257 CrossrefGoogle Scholar
  • 23 H. Jang, W.-S. Lee, H. Nojiri, S. Matsuzawa, H. Yasumura, L. Nie, A. V. Maharaj, S. Gerber, Y.-J. Liu, A. Mehta, D. A. Bonn, R. Liang, W. N. Hardy, C. A. Burns, Z. Islam, S. Song, J. Hastings, T. P. Devereaux, Z.-X. Shen, S. A. Kivelson, C.-C. Kao, D. Zhu, and J.-S. Lee, Proc. Natl. Acad. Sci. U.S.A. 113, 14645 (2016). 10.1073/pnas.1612849113 CrossrefGoogle Scholar
  • 24 J. Choi, O. Ivashko, E. Blackburn, R. Liang, D. A. Bonn, W. N. Hardy, A. T. Holmes, N. B. Christensen, M. Hücker, S. Gerber, O. Gutowski, U. Rütt, M. v. Zimmermann, E. M. Forgan, S. M. Hayden, and J. Chang, Nat. Commun. 11, 990 (2020). 10.1038/s41467-020-14536-1 CrossrefGoogle Scholar
  • 25 E. M. Forgan, E. Blackburn, A. T. Holmes, A. K. R. Briffa, J. Chang, L. Bouchenoire, S. D. Brown, R. Liang, D. Bonn, W. N. Hardy, N. B. Christensen, M. v. Zimmermann, M. Hücker, and S. M. Hayden, Nat. Commun. 6, 10064 (2015). 10.1038/ncomms10064 CrossrefGoogle Scholar
  • 26 C. T. Lin, B. Liang, and H. C. Chen, J. Cryst. Growth 237–239, 778 (2002). 10.1016/S0022-0248(01)02025-5 CrossrefGoogle Scholar
  • 27 N. H. Andersen, M. von Zimmermann, T. Frello, M. Käll, D. Mønster, P. A. Lindgård, J. Madsen, T. Niemöller, H. F. Poulsen, O. Schmidt, J. R. Schneider, T. Wolf, P. Dosanjh, R. Liang, and W. N. Hardy, Physica C 317–318, 259 (1999). 10.1016/S0921-4534(99)00066-0 CrossrefGoogle Scholar
  • 28 M. v. Zimmermann, J. R. Schneider, T. Frello, N. H. Andersen, J. Madsen, M. Käll, H. F. Poulsen, R. Liang, P. Dosanjh, and W. N. Hardy, Phys. Rev. B 68, 104515 (2003). 10.1103/PhysRevB.68.104515 CrossrefGoogle Scholar
  • 29 J. Strempfer, I. Zegkinoglou, U. Rütt, M. v. Zimmermann, C. Bernhard, C. T. Lin, Th. Wolf, and B. Keimer, Phys. Rev. Lett. 93, 157007 (2004). 10.1103/PhysRevLett.93.157007 CrossrefGoogle Scholar
  • 30 A. Q. R. Baron, Y. Tanaka, S. Goto, K. Takeshita, T. Matsushita, and T. Ishikawa, J. Phys. Chem. Solids 61, 461 (2000). 10.1016/S0022-3697(99)00337-6 CrossrefGoogle Scholar
  • 31 B. I. Halperin and C. M. Varma, Phys. Rev. B 14, 4030 (1976). 10.1103/PhysRevB.14.4030 CrossrefGoogle Scholar
  • 32 F. Weber, S. Rosenkranz, J.-P. Castellan, R. Osborn, R. Hott, R. Heid, K.-P. Bohnen, T. Egami, A. H. Said, and D. Reznik, Phys. Rev. Lett. 107, 107403 (2011). 10.1103/PhysRevLett.107.107403 CrossrefGoogle Scholar
  • 33 S. R. Park, T. Fukuda, A. Hamann, D. Lamago, L. Pintschovius, M. Fujita, K. Yamada, and D. Reznik, Phys. Rev. B 89, 020506 (2014). 10.1103/PhysRevB.89.020506 CrossrefGoogle Scholar
  • 34 L. Chaix, G. Ghiringhelli, Y. Y. Peng, M. Hashimoto, B. Moritz, K. Kummer, N. B. Brookes, Y. He, S. Chen, S. Ishida, Y. Yoshida, H. Eisaki, M. Salluzzo, L. Braicovich, Z.-X. Shen, T. P. Devereaux, and W.-S. Lee, Nat. Phys. 13, 952 (2017). 10.1038/nphys4157 CrossrefGoogle Scholar
  • 35 W. S. Lee, Ke-Jin Zhou, M. Hepting, J. Li, A. Nag, A. C. Walters, M. Garcia-Fernandez, H. C. Robarts, M. Hashimoto, H. Lu, B. Nosarzewski, D. Song, H. Eisaki, Z. X. Shen, B. Moritz, J. Zaanen, and T. P. Devereaux, Nat. Phys. 17, 53 (2021). 10.1038/s41567-020-0993-7 CrossrefGoogle Scholar
  • 36 E. Kaneshita, M. Ichioka, and K. Machida, Phys. Rev. Lett. 88, 115501 (2002). 10.1103/PhysRevLett.88.115501 CrossrefGoogle Scholar
  • 37 M. Le Tacon, A. Sacuto, A. Georges, G. Kotliar, Y. Gallais, D. Colson, and A. Forget, Nat. Phys. 2, 537 (2006). 10.1038/nphys362 CrossrefGoogle Scholar
  • 38 G. M. Sheldrick, Acta Crystallogr., Sect. A 64, 112 (2008). 10.1107/S0108767307043930 CrossrefGoogle Scholar
  • 39 V. Petříček, M. Dušek, and L. Palatinus, Z. Kristallogr. Cryst. Mater. 229, 345 (2014). 10.1515/zkri-2014-1737 CrossrefGoogle Scholar
  • 40 R. Arpaia, S. Caprara, R. Fumagalli, G. De Vecchi, Y. Y. Peng, E. Andersson, D. Betto, G. M. De Luca, N. B. Brookes, F. Lombardi, M. Salluzzo, L. Braicovich, C. Di Castro, M. Grilli, and G. Ghiringhelli, Science 365, 906 (2019). 10.1126/science.aav1315 CrossrefGoogle Scholar
  • 41 S. G. Louie, K.-M. Ho, and M. L. Cohen, Phys. Rev. B 19, 1774 (1979). 10.1103/PhysRevB.19.1774 CrossrefGoogle Scholar
  • 42 B. Meyer, C. Elsässer, F. Lechermann, and M. Fähnle, private communication. Google Scholar
  • 43 L. Hedin and B. I. Lundqvist, J. Phys. C 4, 2064 (1971). 10.1088/0022-3719/4/14/022 CrossrefGoogle Scholar
  • 44 K.-P. Bohnen, R. Heid, and M. Krauss, Europhys. Lett. 64, 104 (2003). 10.1209/epl/i2003-00143-x CrossrefGoogle Scholar
  • 45 R. Heid, K.-P. Bohnen, and V. Pankoke, J. Supercond. Novel Magn. 20, 559 (2007). 10.1007/s10948-007-0267-y CrossrefGoogle Scholar
  • 46 R. Heid and K.-P. Bohnen, Phys. Rev. B 60, R3709 (1999). 10.1103/PhysRevB.60.R3709 CrossrefGoogle Scholar