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Fermi surface transformation at the pseudogap critical point of a cuprate superconductor

Nature Physics volume 18, pages 558–564 (2022)Cite this article

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Abstract

The nature of the pseudogap phase remains a major puzzle in our understanding of cuprate high-temperature superconductivity. Whether or not this metallic phase is defined by any of the reported broken symmetries, the topology of its Fermi surface remains a fundamental open question. Here we use angle-dependent magnetoresistance (ADMR) to measure the Fermi surface of the La1.6–xNd0.4SrxCuO4 cuprate. Outside the pseudogap phase, we fit the ADMR data and extract a Fermi surface geometry that is in excellent agreement with angle-resolved photoemission data. Within the pseudogap phase, the ADMR is qualitatively different, revealing a transformation of the Fermi surface. We can rule out changes in the quasiparticle lifetime as the sole cause of this transformation. We find that our data are most consistent with a pseudogap Fermi surface that consists of small, nodal hole pockets, thereby accounting for the drop in carrier density across the pseudogap transition found in several cuprates.

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Fig. 1: ADMR above and below the pseudogap critical doping p* in Nd-LSCO.
Fig. 2: ADMR and FS of Nd-LSCO at p = 0.24.
Fig. 3: Models that fail to account for the change in ADMR across p*.
Fig. 4: FS reconstruction into nodal hole pockets in Nd-LSCO at p = 0.21.

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Data availability

Source data are provided with this paper. Other experimental data presented in this paper are available at http://wrap.warwick.ac.uk/161600/. The results of the conductivity simulations are available from the corresponding author upon reasonable request.

Code availability

The code used to compute the conductivity is available from the corresponding author upon reasonable request.

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Acknowledgements

We acknowledge helpful discussions with J. Analytis, D. Chowdhury, N. Doiron-Leyraud, N. Hussey, M. Kartsovnik, S. Kivelson, D.-H. Lee, S. Lewin, A.-M. Tremblay, K. Modic, S. Musser, C. Proust and S. Todadri. A part of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation (NSF) cooperative agreement no. DMR-1644779 and the State of Florida. P.A.G. acknowledges that this project is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 681260). J.Z. was supported by an NSF grant (MRSEC DMR-1720595). L.T. acknowledges support from the Canadian Institute for Advanced Research (CIFAR) as a Fellow and funding from the Natural Sciences and Engineering Research Council of Canada (NSERC; PIN: 123817), the Fonds de recherche du Québec—Nature et Technologies (FRQNT), the Canada Foundation for Innovation (CFI), and a Canada Research Chair. This research was undertaken thanks in part to funding from the Canada First Research Excellence Fund. Part of this work was funded by the Gordon and Betty Moore Foundation’s EPiQS Initiative (grant GBMF5306 to L.T.). B.J.R. and Y.F. acknowledge funding from the NSF under grant no. DMR-1752784.

Author information

Author notes

  1. These authors contributed equally: Yawen Fang, Gaël Grissonnanche.

Authors and Affiliations

  1. Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, USA

    Yawen Fang, Gaël Grissonnanche, Michael J. Lawler & B. J. Ramshaw

  2. Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY, USA

    Gaël Grissonnanche

  3. Département de physique, Institut quantique, and RQMP, Université de Sherbrooke, Sherbrooke, Québec, Canada

    Gaël Grissonnanche, Anaëlle Legros, Simon Verret, Francis Laliberté, Clément Collignon, Amirreza Ataei, Maxime Dion & Louis Taillefer

  4. SPEC, CEA, CNRS-UMR 3680, Université Paris-Saclay, Gif-sur-Yvette, France

    Anaëlle Legros

  5. Materials Science and Engineering Program, Department of Mechanical Engineering, University of Texas at Austin, Austin, TX, USA

    Jianshi Zhou

  6. National High Magnetic Field Laboratory, Tallahassee, FL, USA

    David Graf

  7. Department of Physics, Applied Physics and Astronomy, Binghamton University, Binghamton, NY, USA

    Michael J. Lawler

  8. Department of Physics, University of Warwick, Coventry, UK

    Paul A. Goddard

  9. Canadian Institute for Advanced Research, Toronto, Ontario, Canada

    Louis Taillefer & B. J. Ramshaw

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Contributions

A.L., P.A.G., L.T. and B.J.R. conceived the experiment. J.Z. grew the samples. A.L., F.L., A.A., C.C. and M.D. performed the sample preparation and characterization. Y.F., G.G., A.L., D.G., P.A.G. and B.J.R. performed the high-magnetic-field measurements at the National High Magnetic Field Laboratory. Y.F., G.G., S.V., M.J.L. and B.J.R. performed the data analysis and simulations. Y.F., G.G., S.V., P.A.G., L.T. and B.J.R. wrote the manuscript with input from all the other co-authors. L.T. and B.J.R. supervised the project.

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Correspondence to B. J. Ramshaw.

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Extended data

Extended Data Fig. 1 Resistivity of Nd-LSCO at p = 0.24 near TSDW.

In-plane resistivity data at B = 35 T as a function of temperature (reproduced from ref. 20). The resistivity ρxx (red line) is perfectly linear over this temperature range without any sign of an upturn or even a change in slope at TSDW = 13 ± 1 K (black arrow) reported by Ma et al.15 at B = 0 T. This suggests that either the SDW is not present in our samples or that the SDW vanishes in a magnetic field and thus does not interfere with our measurements performed at B = 45 T.

Extended Data Fig. 2 Best fit of Nd-LSCO p = 0.21 data with the large, hole-like, unreconstructed Fermi surface.

(a) ADMR data on Nd-LSCO p = 0.21 at T = 25 K and B = 45 T; (b, c) The best fits for the ADMR data in (a) using the band structure ARPES values for Nd-LSCO p = 0.24 with the chemical potential shifted across the van Hove point (at p ≈ 0.23) to p = 0.21, where the Fermi surface is hole-like. Insets represent the scattering rate distribution values over the hole-like Fermi surface at p = 0.21. In (b), the scattering is isotropic over the Fermi surface; in (c) we use the cosine scattering rate model (this figure differs from Fig. 3b because there we only shift the chemical potential, while here we show the best-fit using this model).

Extended Data Fig. 3 Calculation of ADMR for a period three CDW Fermi surface reconstruction.

Calculations using two different gap sizes are shown in (a) and (b), and using a d-wave form factor is shown in (c).

Extended Data Fig. 4 The Hall effect in Nd-LSCO at p = 0.21.

The data is taken at 30 K and is reproduced from Collignon et al.20. ‘h pocket’ is from the fit to the data shown in Fig. 4 of the main text; ‘h+e pocket’ is from a fit that includes both the hole and electron pockets after (π,π) reconstruction; ‘Fermi arcs’ is from the fit in Fig. 3c,d of the main text; ‘e pocket’ is from just the electron pocket produced by (π,π) reconstruction, scaled down by a factor of 20 for clarity.

Extended Data Fig. 5 Variation in the Fermi velocity around the Fermi surface above and below p⋆.

The red curve plots the magnitude of the Fermi velocity around the Fermi surface at p = 0.24, as shown in Fig. 2. The blue curve plots the same quantity for a single nodal hole pocket, as shown in Fig. 4 (the reduction in symmetry is because each nodal hole pocket is 2-fold symmetric). The total anisotropy in vF around the Fermi surface is a factor of 25 at p = 0.24, but just larger than a factor of 2 at p = 0.21.

Extended Data Fig. 6 ADMR experimental set up.

(a) An illustration of the sample mounting. The two samples here are mounted on a G-10 wedge to provide a ϕ angle of 30∘. Additional wedges provided angles of ϕ = 15∘ and 45∘; (b) ADMR as a function of θ angle from − 15∘ to 110∘ and ϕ = 0 at T = 20 K for Nd-LSCO p = 0.24, showing the symmetry of the data about these two angles.

Extended Data Fig. 7 ADMR dependence on the gap amplitude with (π,π) reconstruction.

ADMR calculations with a (π,π) reconstructed Fermi surface for different gap amplitudes at fixed isotropic scattering rate value 1/τ = 22.88 ps−1. Note that this within ≈ 40% of the nodal scattering rate at p = 0.24, consistent with a nodal hole pockets reconstructed from the larger Fermi surface.

Extended Data Fig. 8 ADMR dependence on the scattering rate amplitude with (π,π) reconstruction.

ADMR calculations with a (π,π) reconstructed Fermi surface for different isotropic scattering rate amplitudes at fixed gap value at Δ = 55 K.

Extended Data Table 1 Tight-binding parameters from the fit to the ADMR data at p = 0.24. Best fit tight-binding values for the Nd-LSCO p = 0.24 ADMR data (using the cosine scattering rate model of Equation (4)). The results are extremely close to ARPES tight-binding values reported in Matt et al.22 and Horio et al.34, reproduced here on the second line. Error bars on the AMDR-derived hopping parameters and chemical potential are all ± 0.0005, and were obtained following the procedure described in the above section. The error bar on the value of tz measured by ARPES is ± 0.02t (J. Chang and M. Horio, private communication)
Full size table
Extended Data Table 2 Results of the fit of the Nd-LSCO p = 0.21 data with (π,π) reconstruction. Fit parameter values for Nd-LSCO p = 0.21 plotted in Fig. 4f. The band structure parameters were kept fixed at ARPES values22. Error bars were obtained following the procedure described in the above section
Full size table

Supplementary information

Supplementary Information

Supplementary Figs. 1–3 and Discussion.

Source data

Source Data Fig. 1

Experimental dρ/ρ as a function of θ for several ɸ values.

Source Data Fig. 2

Experimental dρ/ρ as a function of θ for several ɸ values (Fig. 2a). Simulated dρ/ρ as a function of θ for several ɸ values (Fig. 2b). Contours at three values of kz (Fig. 2c).

Source Data Fig. 3

Simulated dρ/ρ as a function of θ for several ɸ values.

Source Data Fig. 4

Experimental dρ/ρ as a function of θ for several ɸ values (Fig. 4a). Simulated dρ/ρ as a function of θ for several ɸ values (Fig. 4b).

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Fang, Y., Grissonnanche, G., Legros, A. et al. Fermi surface transformation at the pseudogap critical point of a cuprate superconductor. Nat. Phys. 18, 558–564 (2022). https://doi.org/10.1038/s41567-022-01514-1

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