Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Chiral phonons in the pseudogap phase of cuprates


The nature of the pseudogap phase of cuprates remains a major puzzle1,2. One of its signatures is a large negative thermal Hall conductivity3, whose origin is as yet unknown. This is observed even in the undoped Mott insulator La2CuO4, in which the charge carriers are localized and therefore cannot be responsible. Here, we show that the thermal Hall conductivity of La2CuO4 is roughly isotropic; that is, for heat transport parallel and normal to the CuO2 planes, it is nearly the same. This shows that the Hall response must come from phonons, as they are the only heat carriers that are able to move with the same ease both normal and parallel to the planes4. For doping levels higher than the critical doping level at which the pseudogap phase ends, both La1.6−xNd0.4SrxCuO4 and La1.8−xEu0.2SrxCuO4 show no thermal Hall signal for a heat current normal to the planes, which establishes that phonons have zero Hall response outside the pseudogap phase. Inside the pseudogap phase, the phonons must become chiral to generate the Hall response, but the mechanism by which this happens remains to be identified. It must be intrinsic (from a coupling of phonons to their electronic environment) rather than extrinsic (from structural defects or impurities), as these are the same on both sides of critical doping.

This is a preview of subscription content

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Thermal Hall conductivity of cuprates at three different dopings.
Fig. 2: Evolution of the c-axis thermal Hall conductivity across the phase diagram.
Fig. 3: Phenomenological fit to the phonon thermal Hall conductivity.

Data availability

All of the data that support the plots in this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.


  1. 1.

    Keimer, B. et al. From quantum matter to high-temperature superconductivity in copper oxides. Nature 518, 179–186 (2015).

    Article  ADS  Google Scholar 

  2. 2.

    Proust, C. & Taillefer, L. The remarkable underlying ground states of cuprate superconductors. Annu. Rev. Condens. Matter Phys. 10, 409–429 (2019).

    Article  ADS  Google Scholar 

  3. 3.

    Grissonnanche, G. et al. Giant thermal Hall conductivity in the pseudogap phase of cuprate superconductors. Nature 571, 376–380 (2019).

    Article  ADS  Google Scholar 

  4. 4.

    Hess, C. et al. Magnon heat transport in doped La2CuO4. Phys. Rev. Lett. 90, 197002 (2003).

    Article  ADS  Google Scholar 

  5. 5.

    Onose, M. et al. Observation of the magnon Hall effect. Science 329, 297–299 (2010).

    Article  ADS  Google Scholar 

  6. 6.

    Katsura, H., Nagaosa, N. & Lee, P. A. Theory of the thermal Hall effect in quantum magnets. Phys. Rev. Lett. 104, 066403 (2010).

    Article  ADS  Google Scholar 

  7. 7.

    Hirschberger, M. et al. Large thermal Hall conductivity of neutral spin excitations in a frustrated quantum magnet. Science 348, 106–109 (2015).

    MathSciNet  Article  ADS  Google Scholar 

  8. 8.

    Lee, H., Han, J. H. & Lee, P. A. Thermal Hall effect of spins in a paramagnet. Phys. Rev. B 91, 125413 (2015).

    Article  ADS  Google Scholar 

  9. 9.

    Qin, T., Zhou, J. & Shi, J. Berry curvature and the phonon Hall effect. Phys. Rev. B 86, 104305 (2012).

    Article  ADS  Google Scholar 

  10. 10.

    Yang, Y.-F., Zhang, G.-M. & Zhang, F.-C. Universal behavior of the anomalous thermal Hall conductivity. Phys. Rev. Lett. 124, 186602 (2020).

    Article  ADS  Google Scholar 

  11. 11.

    Nasu, J., Yoshitake, J. & Motome, Y. Thermal transport in the Kitaev model. Phys. Rev. Lett. 119, 127204 (2017).

    Article  ADS  Google Scholar 

  12. 12.

    Ye, M. et al. Quantization of the thermal Hall conductivity at small Hall angles. Phys. Rev. Lett. 121, 147201 (2018).

    Article  ADS  Google Scholar 

  13. 13.

    Vinkler-Aviv, Y. & Rosch, A. Approximately quantized thermal Hall effect of chiral liquids coupled to phonons. Phys. Rev. X 8, 031032 (2018).

    Google Scholar 

  14. 14.

    Mori, M. et al. Origin of the phonon Hall effect in rare-Earth garnets. Phys. Rev. Lett. 113, 265901 (2014).

    Article  ADS  Google Scholar 

  15. 15.

    Ideue, T. et al. Giant thermal Hall effect in multiferroics. Nat. Mater. 16, 797–802 (2017).

    Article  ADS  Google Scholar 

  16. 16.

    Li, X. et al. Phonon thermal Hall effect in strontium titanate. Phys. Rev. Lett. 124, 105901 (2020).

    Article  ADS  Google Scholar 

  17. 17.

    Samajdar, R. et al. Enhanced thermal Hall effect in the square-lattice Néel state. Nat. Phys. 15, 1290–1294 (2019).

    Article  Google Scholar 

  18. 18.

    Han, J. H., Park, J.-H. & Lee, P. A. Consideration of thermal Hall effect in undoped cuprates. Phys. Rev. B 99, 205157 (2019).

    Article  ADS  Google Scholar 

  19. 19.

    Chen, J.-Y., Kivelson, S. A. & Sun, X.-Q. Enhanced thermal Hall effect in nearly ferroelectric insulators. Phys. Rev. Lett. 124, 167601 (2020).

    Article  ADS  Google Scholar 

  20. 20.

    Collignon, C. et al. Fermi-surface transformation across the pseudogap critical point of the cuprate superconductor La2−xNd0.4SrxCuO4. Phys. Rev. B 95, 224517 (2017).

    Article  ADS  Google Scholar 

  21. 21.

    Matt, C. E. et al. Electron scattering, charge order and pseudogap physics in La2−xNd0.4SrxCuO4: an angle-resolved photoemission spectroscopy study. Phys. Rev. B 92, 134524 (2015).

    Article  ADS  Google Scholar 

  22. 22.

    Michon, B. et al. Thermodynamic signatures of quantum criticality in cuprate superconductors. Nature 567, 281–222 (2019).

    Article  Google Scholar 

  23. 23.

    Strohm, C., Rikken, G. L. J. A. & Wyder, P. Phenomenological evidence for the phonon Hall effect. Phys. Rev. Lett. 95, 155901 (2005).

    Article  ADS  Google Scholar 

  24. 24.

    He, Y. et al. Rapid change in superconductivity and electron-phonon coupling through the critical point in Bi-2212. Science 362, 62–65 (2019).

    Article  ADS  Google Scholar 

  25. 25.

    Kyung, B. et al. Pseudogap induced by short-range spin correlations in a doped Mott insulator. Phys. Rev. B 73, 165114 (2006).

    Article  ADS  Google Scholar 

  26. 26.

    Scheurer, M. S. et al. Topological order in the pseudogap metal. Proc. Natl Acad. Sci. USA 115, E3665–E3672 (2018).

    MathSciNet  Article  Google Scholar 

  27. 27.

    Hunt, A. W. et al. Glassy slowing of stripe modulation in (La,Eu,Nd)2−x(Sr,Ba)xCuO4: a 63Cu and 139La NQR study down to 350 mK. Phys. Rev. B 64, 134525 (2001).

    Article  ADS  Google Scholar 

  28. 28.

    Frachet, M. et al. Hidden magnetism at the pseudogap critical point of a high-temperature superconductor. Preprint at (2019).

  29. 29.

    Ye, M. et al. Phonon dynamics in the Kitaev spin liquid. Preprint at (2020).

  30. 30.

    Hirokane, Y. et al. Phononic thermal Hall effect in diluted terbium oxides. Phys. Rev. B 99, 134419 (2019).

    Article  ADS  Google Scholar 

  31. 31.

    Kasahara, Y. et al. Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid. Nature 559, 227–231 (2018).

    Article  ADS  Google Scholar 

  32. 32.

    Hentrich, R. et al. Large thermal Hall effect in α-RuCl3: Evidence for heat transport by Kitaev-Heisenberg paramagnons. Phys. Rev. B 99, 085136 (2019).

    Article  ADS  Google Scholar 

  33. 33.

    Cyr-Choinière, O. et al. Pseudogap temperature T* of cuprate superconductors from the Nernst effect. Phys. Rev. B 97, 064502 (2018).

    Article  ADS  Google Scholar 

  34. 34.

    Grissonnanche, G. et al. Wiedemann–Franz law in the underdoped cuprate superconductor YBCO. Phys. Rev. B 93, 064513 (2016).

    Article  ADS  Google Scholar 

  35. 35.

    Daou, R. et al. Linear temperature dependence of resistivity and change in the Fermi surface at the pseudogap critical point of a high-Tc superconductor. Nat. Phys. 5, 31–34 (2009).

    Article  Google Scholar 

  36. 36.

    Axe, J. D. & Crawford, M. K. Structural instabilities in lanthanum cuprate superconductors. J. Low Temp. Phys. 95, 271–284 (1994).

    Article  ADS  Google Scholar 

Download references


We thank L. Balents, K. Behnia, R. M. Fernandes, I. Garate, J. H. Han, C. Hess, S. A. Kivelson, P. A. Lee, A. H. MacDonald, J. E. Moore, B. J. Ramshaw, L. Savary, O. Sushkov, A.-M. S. Tremblay, R. Valenti and C. M. Varma for fruitful discussions. 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 EPiQS Initiative of the Gordon and Betty Moore Foundation (Grant GBMF5306 to L.T.). J.-S.Z. was supported by a US National Science Foundation grant (MRSEC DMR-1720595).

Author information




G.G., S.T., M.-E.B. and E.L. performed the thermal Hall conductivity measurements. A.G., A.A., F.L., M.D. and N.D.-L. prepared and characterized the samples. J.-S.Z. grew the Nd-LSCO single crystals. S.P., T.T. and H.T. grew the Eu-LSCO and La2CuO4 single crystals. G.G. and L.T. wrote the manuscript, in consultation with all of the authors. L.T. supervised the project.

Corresponding authors

Correspondence to G. Grissonnanche or L. Taillefer.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Peer review information Nature Physics thanks Liling Sun and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Extended data

Extended Data Fig. 1 Current and field orientation for κxy and κzy measurements.

Sketch of the thermal Hall measurement setup for a) J // a // -x and b) J // c // z. The Cartesian coordinate system is defined in the same way for the two samples.

Extended Data Fig. 2 Longitudinal thermal conductivities κxx and κzz in La2CuO4.

Thermal conductivity versus temperature in a field of magnitude H = 15 T for La2CuO4 (p = 0), plotted as a) κnn vs T and b) κnn / T vs T, for heat current directions J // a (n = x; blue) and J // c (n = z; red). The longitudinal thermal conductivity of phonons at low temperature is nearly isotropic, with κxx / κzz = κa / κc ~ 0.8 at T = 25 K.

Extended Data Fig. 3 Longitudinal thermal conductivities κxx and κzz in Nd-LSCO.

Thermal conductivity κnn versus temperature in a field of magnitude H = 15 T, plotted as κnn / T vs T, for a) Nd-LSCO with p = 0.21 and b) Nd-LSCO with p = 0.24, for heat current directions J // a (n = x; blue) and J // c (n = z; red). In panels c) and d), the thermal conductivity of charge carriers is subtracted, using the Wiedemann-Franz law to estimate its magnitude (see ref. 3). The longitudinal thermal conductivity of phonons at low temperature is nearly isotropic, with κxx / κzz = κa / κc ~ 1.2 and 1.3 at T = 25 K, for p = 0.21 and p = 0.24, respectively.

Extended Data Fig. 4 Anisotropy of electrical Hall conductivity in Nd-LSCO.

Electrical Hall conductivity σny versus temperature in a field of magnitude H = 15 T, plotted as L0 σny vs T, for Nd-LSCO with p = 0.24, for heat current directions J // a (n = x; blue) and J // c (n = z; red). The data for σzy are multiplied by a factor 250. We use the approximate relation σzy = ρzy / (ρzz ρxx), with ρzz and ρxx data taken from ref. 35. The σxy data are taken from ref. 3.

Extended Data Fig. 5 Electronic thermal Hall conductivity in Nd-LSCO p = 0.24.

Estimate of the maximal c-axis thermal Hall conductivity from charge carriers in our sample of Nd-LSCO with p = 0.24, obtained by applying the Wiedemann-Franz law to the measured electrical Hall conductivity σzy, namely κzy / TL0 σzy, where σzy ≤ ρzy / (ρzz ρyy). a) Electrical resistivity for J // c, ρzz vs T (from ref. 35); b) electrical Hall resistivity for J // c and H // a, ρzy vs T ; c) maximal electrical Hall conductivity for J // c and H // a, defined as σzy = ρzy / (ρzz ρxx) (with ρxx data from ref. 35), plotted as L0 σzy (multiplied by 60) vs T ; d) comparison of the measured electrical (σzy) and thermal (κzy) Hall conductivities, plotted as L0 σzy (blue) and κzy / T (red; Fig. 1b) vs T.

Extended Data Fig. 6 Field dependence of κzz and κzy in La2CuO4 and Nd-LSCO.

Upper panels: thermal conductivity κzz measured at H = 0 T (purple), 10 T (green) and 15 T (red), plotted as κzz / T vs T, for a) La2CuO4, b) Nd-LSCO with p = 0.21 and c) Nd-LSCO with p = 0.24. Lower panels: thermal Hall conductivity κzy measured at H = 10 T (purple) and 15 T (red), plotted as κzy / (T H) vs T, for d) La2CuO4, e) Nd-LSCO with p = 0.21 and f) Nd-LSCO with p = 0.24. We see that κzy is approximately linear in H.

Extended Data Fig. 7 Structural transition in Nd-LSCO.

a) Structural phase diagram of Nd-LSCO as a function of doping. The black dots and black line mark the structural transition from the LTO1 phase to the LTT phase at low temperature, at TLTT, as measured by x-ray diffraction36. The squares mark TLTT in our samples with p = 0.21 (blue) and p = 0.24 (green), as detected by dilatometry measurements (see panel b). b) Change in sample length L as a function of temperature, plotted as its derivative dL / dT vs T, measured in our c-axis sample of Nd-LSCO with p = 0.21 (blue) and in a sample of Nd-LSCO cut from the same large single crystal as, and next to, our c-axis sample of Nd-LSCO with p = 0.24 (green). The dip in the curves marks the structural phase transition from the LTO1 phase above to the LTT phase below the transition temperature TLTT, where TLTT = 82 ± 5 K at p = 0.21 and TLTT = 45 ± 10 K at p = 0.24. The error bars on the two values of TLTT correspond to the full width of each corresponding dip. These data confirm that our two Nd-LSCO samples, with p = 0.21 and p = 0.24, have the same crystal structure. This shows that all the differences observed in their properties, in particular the dramatic difference in their thermal Hall conductivity κzy (Fig. 1), are not due to a difference in structural properties. Instead, these differences are linked with the onset of the pseudogap phase at p* = 0.23.

Source data

Source Data Fig. 1

Source data for Figure 1

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Grissonnanche, G., Thériault, S., Gourgout, A. et al. Chiral phonons in the pseudogap phase of cuprates. Nat. Phys. 16, 1108–1111 (2020).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing