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Mirror symmetry breaking in a model insulating cuprate


Among the most actively studied issues in the cuprates are the natures of the pseudogap and strange metal states and their relationship to superconductivity1. There is general agreement that the low-energy physics of the Mott-insulating parent state is well captured by a two-dimensional spin S = 1/2 antiferromagnetic Heisenberg model2. However, recent observations of a large thermal Hall conductivity in several parent cuprates appear to defy this simple model and suggest proximity to a magneto-chiral state that breaks all mirror planes that are perpendicular to the CuO2 layers3,4,5,6. Here we use optical second harmonic generation to directly resolve the point group symmetries of the model parent cuprate Sr2CuO2Cl2. We report evidence of an order parameter that breaks all perpendicular mirror planes and is consistent with a magneto-chiral state in zero magnetic field. Although this order is clearly coupled to the antiferromagnetism, we are unable to realize its time-reversed partner by thermal cycling through the antiferromagnetic transition temperature or by sampling different spatial locations. This suggests that the order onsets above the Néel temperature and may be relevant to the mechanism of pseudogap formation.

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Fig. 1: SHG from Sr2CuO2Cl2.
Fig. 2: Mirror symmetry breaking in the AFM state.
Fig. 3: Temperature dependence of the SHG response.
Fig. 4: Order parameter symmetry and spatial dependence.

Data availability

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


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We acknowledge helpful conversations with D. Kennes, S. Kivelson, P. Lee, O. Motrunich, D. Pelc and K. Plumb. We also thank L. Taillefer and G. Grissonnanche for sharing unpublished data. The SHG work is supported by an ARO PECASE award W911NF-17-1-0204. D.H. also acknowledges support for instrumentation from the David and Lucile Packard Foundation and from the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center (PHY-1733907). A.d.l.T. acknowledges support from the Swiss National Science Foundation through an Early Postdoc Mobility Fellowship (P2GEP2_165044). K.L.S. acknowledges a Caltech Prize Postdoctoral Fellowship. S.S. acknowledges support from NSF grant DMR-2002850. M.S.S. acknowledges support from the German National Academy of Sciences Leopoldina through Grant LPDS 2016-12. M.R.N. was supported by the Materials Sciences and Engineering Division, Basic Energy Sciences, Office of Science, US Department of Energy. The work at the University of Minnesota was funded by the US Department of Energy through the University of Minnesota Center for Quantum Materials, under grant no. DE-SC-0016371.

Author information




A.d.l.T., L.Z., D.H. and M.G. conceived the experiment. A.d.l.T., K.L.S. and L.Z. performed the optical measurements. Y.L. and B.Y. synthesized, characterized and aligned the samples. A.d.l.T., L.Z. and D.H. analysed the data. S.D.M., M.S.S., S.S. and M.R.N. performed the theoretical calculations and, together with A.d.l.T. and D.H., interpreted the results. A.d.l.T. and D.H. wrote the manuscript with input from all authors.

Corresponding author

Correspondence to D. Hsieh.

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Peer review informationNature Physics thanks Manfred Fiebig and Marco Grioni for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–9 and Sections 1–12.

Source data

Source Data Fig. 2

RA-SHG data.

Source Data Fig. 3

Single angle temperature dependence data.

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Torre, A.d.l., Seyler, K.L., Zhao, L. et al. Mirror symmetry breaking in a model insulating cuprate. Nat. Phys. 17, 777–781 (2021).

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