Critical Doping for the Onset of Fermi-Surface Reconstruction by Charge-Density-Wave Order in the Cuprate Superconductor ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$

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Critical Doping for the Onset of Fermi-Surface Reconstruction by Charge-Density-Wave Order in the Cuprate Superconductor ${La}_{2 - x} {Sr}_{x} {CuO}_{4}$

S. Badoux, S. A. A. Afshar, B. Michon, A. Ouellet, S. Fortier, D. LeBoeuf, T. P. Croft, C. Lester, S. M. Hayden, H. Takagi, K. Yamada, D. Graf, N. Doiron-Leyraud, and Louis Taillefer

Phys. Rev. X 6, 021004 – Published 6 April 2016

Abstract

The Seebeck coefficient $S$ of the cuprate superconductor ${La}_{2 - x} {Sr}_{x} {CuO}_{4}$ (LSCO) was measured in magnetic fields large enough to access the normal state at low temperatures, for a range of Sr concentrations from $x = 0.07$ to $x = 0.15$ . For $x = 0.11$ , 0.12, 0.125, and 0.13, $S / T$ decreases upon cooling to become negative at low temperatures. The same behavior is observed in the Hall coefficient $R_{H} (T)$ . In analogy with other hole-doped cuprates at similar hole concentrations $p$ , the negative $S$ and $R_{H}$ 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 $0.085 < p < 0.15$ . We argue that in the field-induced normal state of LSCO, charge-density-wave order ends at a critical doping $p_{CDW} = 0.15 \pm 0.005$ , well below the pseudogap critical doping $p^{⋆} ≃ 0.19$ .

Received 18 November 2015

DOI:https://doi.org/10.1103/PhysRevX.6.021004

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Charge density waves

High-temperature superconductors

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

S. Badoux^1,*, S. A. A. Afshar¹, B. Michon¹, A. Ouellet¹, S. Fortier¹, D. LeBoeuf², T. P. Croft³, C. Lester³, S. M. Hayden³, H. Takagi⁴, K. Yamada⁵, D. Graf⁶, N. Doiron-Leyraud¹, and Louis Taillefer^1,7,†

¹Département de Physique & RQMP, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1, Canada
²Laboratoire National des Champs Magnétiques Intenses, UPR 3228, (CNRS-INSA-UJF-UPS), Grenoble 38042, France
³H. H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom
⁴Department of Advanced Materials, University of Tokyo, Kashiwa 277-8561, Japan
⁵Institute of Materials Structure Science, High Energy Accelerator Research Organization & The Graduate University for Advanced Studies, Oho, Tsukuba 305-0801, Japan
⁶National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA
⁷Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada

^*sven.badoux@usherbrooke.ca
^†louis.taillefer@usherbrooke.ca

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 ${La}_{2 - x} {Sr}_{x} {CuO}_{4}$ to show that these phases are separate.

Prior electrical resistivity measurements on ${La}_{2 - x} {Sr}_{x} {CuO}_{4}$ in very high magnetic fields revealed that its pseudogap phase terminates at a critical doping level of $x \sim 0.19$ in the absence of superconductivity. We measure the thermopower of single crystals of ${La}_{2 - x} {Sr}_{x} {CuO}_{4}$ 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 $x = 0.07$ to $x = 0.15$ . Around $x \sim 0.12$ , 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 ${La}_{2 - x} {Sr}_{x} {CuO}_{4}$ ends at $x \sim 0.15$ . 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.

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Vol. 6, Iss. 2 — April - June 2016

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Figure 1
Temperature-doping phase diagram of the cuprate superconductors YBCO (a) and LSCO (b). The superconducting transition temperature $T_{c}$ is drawn as a black line. CDW modulations are detected by x-ray diffraction below $T_{CDW}$ (green triangles) in YBCO (up triangles [11], down triangles [12]) and LSCO (up triangles [13], down triangle [14]). SDW modulations are detected by neutron diffraction below $T_{SDW}$ (blue squares) in YBCO [15] and LSCO [16, 17, 18, 19, 20]. When plotted as $S / T$ vs $T$ , the normal-state Seebeck coefficient peaks at a temperature $T_{\max}$ (full red circles) before it drops at low temperatures because of Fermi-surface reconstruction (YBCO, Ref. [6]; LSCO, this work, Figs. 3 and 4). A similar $T_{\max}$ can also be defined for the Hall coefficient (open red circles), below which $R_{H}$ $(T)$ drops at low temperatures (YBCO, Ref. [4]).
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Figure 2
Isotherms of the Seebeck coefficient in LSCO, plotted as $S / T$ vs magnetic field $H$ , at various temperatures, as indicated, for six samples, with $x = 0.07$ (a), $x = 0.085$ (b), $x = 0.125$ (c), $x = 0.13$ (d), $x = 0.144$ (e), and $x = 0.15$ (f). For $x = 0.125$ and 0.13, $S / T$ at high $H$ decreases at low temperatures, to reach negative values. For $x = 0.144$ , $S / T$ also decreases at low temperatures, below 15 K. This decrease is the signature of FSR. In contrast, for $x = 0.07$ and 0.15, $S / T$ at the highest measured field keeps increasing with decreasing temperature down to the lowest temperature. This shows that there is no FSR at those dopings, at least down to 4 K and 9 K, respectively. The same is true at $x = 0.085$ , at least down to 15 K.
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Figure 3
Seebeck coefficient of LSCO, plotted as $S / T$ vs temperature $T$ , measured in a magnetic field $H = 0$ (open circles), 16 T (full circles), and 34 T (squares), for four samples, with $x = 0.07$ and 0.125 (a), and $x = 0.144$ and 0.15 (b). The data in panel (b) are normalized to their value at $T = 100 K$ . All data points represent the normal state, for which the solid lines are a guide to the eye, except the lowest point for each of $x = 0.144$ and $x = 0.15$ [panel (b)]. For these two points, the isotherms are still going up the superconducting transition (Fig. 2). The dashed lines are an extension of the normal-state behavior based on extrapolating those isotherms beyond 34 T. $T_{\max}$ marks the temperature below which $S / T$ decreases at low temperatures (arrow), in some cases reaching negative values, as seen here for $x = 0.125$ . This decrease is the signature of FSR. Note how the data for $x = 0.144$ and $x = 0.15$ split below $T ≃ 30 K$ , with the former dropping at low $T$ because of FSR and the latter showing no decrease, and hence no FSR (at least down to 9 K).
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Figure 4
Same as in Fig. 3, for samples with $x = 0.11$ (yellow), $x = 0.12$ (blue), $x = 0.125$ (red), and $x = 0.13$ (green), measured at $H = 16 T$ (full circles), 17.5 T (open squares), and 44 T (full squares). The data in panel (b) are normalized to their value at $T = 100 K$ . FSR is clearly observed in all four samples, as a drop in $S / T$ at low temperature. Inset of panel (b): Isotherm at $T = 8 K$ for $x = 0.12$ , showing that $S / T$ becomes increasingly negative with an increasing field, demonstrating that the negative $S$ is a property of the normal state.
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Figure 5
Comparison of LSCO (red) and YBCO (green) at $p = 0.12$ . (a) Temperature dependence of the x-ray intensity associated with the CDW modulations, normalized at $T_{c}$ , detected in LSCO [13] and YBCO [10]. Lines are a guide to the eye. The cusp is at $T_{c}$ . (b) Normal-state Seebeck coefficient of LSCO (this work) and YBCO [6], measured in a magnetic field as indicated, plotted as $S / T$ vs $T$ . $T_{\max}$ is the temperature below which $S / T$ drops to reach negative values at low temperatures (arrow), the signature of FSR. This $T_{\max}$ is plotted as full circles in Fig. 1. Lines are a guide to the eye. (c) Hall coefficient of LSCO at $H = 16 T$ and YBCO at $H = 15 T$ [2], plotted as $e R_{H} / V$ , where $e$ is the electron charge and $V$ the volume per planar Cu atom. $T_{\max}$ is the temperature below which $R_{H} (T)$ drops to reach negative values at low temperatures (arrow), another signature of FSR. $T_{\max}$ is plotted as open circles in Fig. 1(a) [4].
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Physical Review X

Critical Doping for the Onset of Fermi-Surface Reconstruction by Charge-Density-Wave Order in the Cuprate Superconductor La2−xSrxCuO4

S. Badoux, S. A. A. Afshar, B. Michon, A. Ouellet, S. Fortier, D. LeBoeuf, T. P. Croft, C. Lester, S. M. Hayden, H. Takagi, K. Yamada, D. Graf, N. Doiron-Leyraud, and Louis Taillefer

Phys. Rev. X 6, 021004 – Published 6 April 2016

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Critical Doping for the Onset of Fermi-Surface Reconstruction by Charge-Density-Wave Order in the Cuprate Superconductor ${La}_{2 - x} {Sr}_{x} {CuO}_{4}$