- Open Access
Critical Doping for the Onset of Fermi-Surface Reconstruction by Charge-Density-Wave Order in the Cuprate Superconductor
Phys. Rev. X 6, 021004 – Published 6 April, 2016
DOI: https://doi.org/10.1103/PhysRevX.6.021004
Abstract
The Seebeck coefficient of the cuprate superconductor (LSCO) was measured in magnetic fields large enough to access the normal state at low temperatures, for a range of Sr concentrations from to . For , 0.12, 0.125, and 0.13, decreases upon cooling to become negative at low temperatures. The same behavior is observed in the Hall coefficient . In analogy with other hole-doped cuprates at similar hole concentrations , the negative and show that the Fermi surface of LSCO undergoes a reconstruction caused by the onset of charge-density-wave modulations. Such modulations have indeed been detected in LSCO by x-ray diffraction in precisely the same doping range. Our data show that in LSCO this Fermi-surface reconstruction is confined to . We argue that in the field-induced normal state of LSCO, charge-density-wave order ends at a critical doping , well below the pseudogap critical doping .
Physics Subject Headings (PhySH)
Popular Summary
Copper-oxide materials known as cuprates act as superconductors at record-high temperatures. The origin of this remarkable phenomenon, discovered three decades ago, remains an outstanding puzzle in condensed-matter physics, largely because cuprates exhibit a number of intriguing electronic phases that are intertwined in ways that we do not yet understand. One of these phases is characterized by modulations in the density of charge carriers, known as a charge density wave. Another fundamental phase of cuprates is the pseudogap phase, which remains unexplained to this day. A key open question is whether the two phases are intimately linked or separate. Here, we use transport experiments on the classic cuprate material to show that these phases are separate.
Prior electrical resistivity measurements on in very high magnetic fields revealed that its pseudogap phase terminates at a critical doping level of in the absence of superconductivity. We measure the thermopower of single crystals of in high magnetic fields (up to 45 T) as a way to track the charge-density-wave order with doping via the profound effect it has on the Fermi surface. We examine a range of Sr concentrations from to . Around , we observe a negative Seebeck coefficient at low temperature, a well-established signature of the charge-density wave in cuprates. As the doping level increases, this signature disappears; we find that the charge-density-wave phase in ends at . The fact that with decreased doping the pseudogap phase sets in well before the charge-density-wave order implies that the origin of the enigmatic pseudogap is independent of charge-density-wave formation.
We expect that our findings will motivate future investigations focusing on the nature of the pseudogap in cuprates.
Article Text
References (33)
- N. Doiron-Leyraud, C. Proust, D. LeBoeuf, J. Levallois, J.-B. Bonnemaison, R. Liang, D. A. Bonn, W. N. Hardy, and L. Taillefer, Quantum Oscillations and the Fermi Surface in an Underdoped High- Superconductor, Nature (London) 447, 565 (2007).
- D. LeBoeuf, N. Doiron-Leyraud, J. Levallois, R. Daou, J.-B. Bonnemaison, N. E. Hussey, L. Balicas, B. J. Ramshaw, R. Liang, D. A. Bonn et al., Electron Pockets in the Fermi Surface of Hole-Doped High- Superconductors, Nature (London) 450, 533 (2007).
- L. Taillefer, Fermi Surface Reconstruction in High- Superconductors, J. Phys. Condens. Matter 21, 164212 (2009).
- D. LeBoeuf, N. Doiron-Leyraud, B. Vignolle, M. Sutherland, B. J. Ramshaw, J. Levallois, R. Daou, F. Laliberté, O. Cyr-Choinière, J. Chang et al., Lifshitz Critical Point in the Cuprate Superconductor from High-Field Hall Effect Measurements, Phys. Rev. B 83, 054506 (2011).
- J. Chang, R. Daou, C. Proust, D. LeBoeuf, N. Doiron-Leyraud, F. Laliberté, B. Pingault, B. J. Ramshaw, R. Liang, D. A. Bonn et al., Nernst and Seebeck Coefficients of the Cuprate Superconductor : A Study of Fermi Surface Reconstruction, Phys. Rev. Lett. 104, 057005 (2010).
- F. Laliberté, J. Chang, N. Doiron-Leyraud, E. Hassinger, R. Daou, M. Rondeau, B. J. Ramshaw, R. Liang, D. A. Bonn, W. N. Hardy et al., Fermi-Surface Reconstruction by Stripe Order in Cuprate Superconductors, Nat. Commun. 2, 432 (2011).
- J. Fink, V. Soltwisch, J. Geck, E. Schierle, E. Weschke, and B. Buchner, Phase Diagram of Charge Order in from Resonant Soft X-Ray Diffraction, Phys. Rev. B 83, 092503 (2011).
- T. Wu, H. Mayaffre, S. Krämer, M. Horvatić, C. Berthier, W. N. Hardy, R. Liang, D. A. Bonn, and M.-H. Julien, Magnetic-Field-Induced Charge-Stripe Order in the High-Temperature Superconductor , Nature (London) 477, 191 (2011).
- G. Ghiringhelli, M. Le Tacon, M. Minola, S. Blanco-Canosa, C. Mazzoli, N. B. Brookes, G. M. De Luca, A. Frano, D. G. Hawthorn, F. He et al., Long-Range Incommensurate Charge Fluctuations in , Science 337, 821 (2012).
- J. Chang, E. Blackburn, A. T. Holmes, N. B. Christensen, J. Larsen, J. Mesot, R. Liang, D. A. Bonn, W. N. Hardy, A. Watenphul et al., Direct Observation of Competition between Superconductivity and Charge Density Wave Order in , Nat. Phys. 8, 871 (2012).
- M. Hücker, N. B. Christensen, A. T. Holmes, E. Blackburn, E. M. Forgan, R. Liang, D. A. Bonn, W. N. Hardy, O. Gutowski, M. v. Zimmermann, S. M. Hayden, and J. Chang, Competing Charge, Spin, and Superconducting Orders in Underdoped , Phys. Rev. B 90, 054514 (2014).
- S. Blanco-Canosa, A. Frano, E. Schierle, J. Porras, T. Loew, M. Minola, M. Bluschke, E. Weschke, B. Keimer, and M. Le Tacon, Resonant X-Ray Scattering Study of Charge-Density Wave Correlations in , Phys. Rev. B 90, 054513 (2014).
- T. P. Croft, C. Lester, M. S. Senn, A. Bombardi, and S. M. Hayden, Charge Density Wave Fluctuations in and Their Competition with Superconductivity, Phys. Rev. B 89, 224513 (2014).
- N. B. Christensen, J. Chang, J. Larsen, M. Fujita, M. Oda, M. Ido, N. Momono, E. M. Forgan, A. T. Holmes, J. Mesot, M. Huecker, and M. v. Zimmermann, Bulk Charge Stripe Order Competing with Superconductivity in (), arXiv:1404.3192.
- D. Haug, V. Hinkov, Y. Sidis, P. Bourges, N. B. Christensen, A. Ivanov, T. Keller, C. T. Lin, and B. Keimer, Neutron Scattering Study of the Magnetic Phase Diagram of Underdoped , New J. Phys. 12, 105006 (2010).
- J. Chang, Ch. Niedermayer, R. Gilardi, N. B. Christensen, H. M. Ronnow, D. F. McMorrow, M. Ay, J. Stahn, O. Sobolev, A. Hiess et al., Tuning Competing Orders in Cuprate Superconductors by the Application of an External Magnetic Field, Phys. Rev. B 78, 104525 (2008).
- M. Kofu, S.-H. Lee, M. Fujita, H.-J. Kang, H. Eisaki, and K. Yamada, Hidden Quantum Spin-Gap State in the Static Stripe Phase of High-Temperature Superconductors, Phys. Rev. Lett. 102, 047001 (2009).
- S. Wakimoto, G. Shirane, Y. Endoh, K. Hirota, S. Ueki, K. Yamada, R. J. Birgeneau, M. A. Kastner, Y. S. Lee, P. M. Gehring, and S. H. Lee, Observation of Incommensurate Magnetic Correlations at the Lower Critical Concentration for Superconductivity in (), Phys. Rev. B 60, R769 (1999).
- B. Lake, H. M. Rønnow, N. B. Christensen, G. Aeppli, K. Lefmann, D. F. McMorrow, P. Vorderwisch, P. Smeibidl, N. Mangkorntong, T. Sasagawa et al., Antiferromagnetic Order Induced by an Applied Magnetic Field in a High-Temperature Superconductor, Nature (London) 415, 299 (2002).
- H. Kimura, K. Hirota, H. Matsushita, K. Yamada, Y. Endoh, S-H. Lee, C. F. Majkrzak, R. Erwin, G. Shirane, M. Greven et al., Neutron-Scattering Study of Static Antiferromagnetic Correlations in , Phys. Rev. B 59, 6517 (1999).
- 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 , Nat. Commun. 6, 6438 (2015).
- N. Doiron-Leyraud, S. Lepault, O. Cyr-Choinière, B. Vignolle, G. Grissonnanche, F. Laliberté, J. Chang, N. Barišić, M. K. Chan, L. Ji et al., Hall, Seebeck, and Nernst Coefficients of Underdoped : Fermi-Surface Reconstruction in an Archetypal Cuprate Superconductor, Phys. Rev. X 3, 021019 (2013).
- N. Barišić, S. Badoux, M. K. Chan, C. Dorow, W. Tabis, B. Vignolle, G. Yu, J. Béard, X. Zhao, C. Proust, and M. Greven, Universal Quantum Oscillations in the Underdoped Cuprate Superconductors, Nat. Phys. 9, 761 (2013).
- W. Tabis, Y. Li, M. Le Tacon, L. Braicovich, A. Kreyssig, M. Minola, G. Dellea, E. Weschke, M. J. Veit, M. Ramazanoglu et al., Charge Order and Its Connection with Fermi-Liquid Charge Transport in a Pristine High- Cuprate, Nat. Commun. 5, 5875 (2014).
- V. Thampy, M. P. M. Dean, N. B. Christensen, L. Steinke, Z. Islam, M. Oda, M. Ido, N. Momono, S. B. Wilkins, and J. P. Hill, Rotated Stripe Order and Its Competition with Superconductivity in , Phys. Rev. B 90, 100510 (2014).
- R. A. Cooper, Y. Wang, B. Vignolle, O. J. Lipscombe, S. M. Hayden, Y. Tanabe, T. Adachi, Y. Koike, M. Nohara, H. Takagi, C. Proust, and N. E. Hussey, Anomalous Criticality in the Electrical Resistivity of , Science 323, 603 (2009).
- T. Suzuki, T. Goto, K. Chiba, M. Minami, Y. Oshima, T. Fukase, M. Fujita, and K. Yamada, Hall Coefficient of () at Low Temperatures under High Magnetic Fields, Phys. Rev. B 66, 104528 (2002).
- F. F. Balakirev, J. B. Betts, A. Migliori, I. Tsukada, Y. Ando, and G. S. Boebinger, Quantum Phase Transition in the Magnetic-Field-Induced Normal State of Optimum-Doped High- Cuprate Superconductors at Low Temperatures, Phys. Rev. Lett. 102, 017004 (2009).
- O. Cyr-Choinière, R. Daou, F. Laliberté, D. LeBoeuf, N. Doiron-Leyraud, J. Chang, J.-Q. Yan, J.-G. Cheng, J.-S. Zhou, J. B. Goodenough et al., Enhancement of the Nernst Effect by Stripe Order in a High- Superconductor, Nature (London) 458, 743 (2009).
- T. Noda, H. Eisaki, and S. Uchida, Evidence for One-Dimensional Charge Transport in , Science 286, 265 (1999).
- K. B. Efetov, H. Meier, and C. Pépin, Pseudogap State Near a Quantum Critical Point, Nat. Phys. 9, 442 (2013).
- T. P. Croft and S. M. Hayden (private communication).
- S. Badoux, W. Tabis, F. Laliberté, G. Grissonnanche, B. Vignolle, D. Vignolles, J. Béard, D. A. Bonn, W. N. Hardy, R. Liang et al., Change of Carrier Density at the Pseudogap Critical Point of a Cuprate Superconductor, Nature (London) 531, 210 (2016).
