Abstract
Identifying ordered phases and their underlying symmetries in materials that exhibit high-temperature superconductivity is an important step towards understanding the mechanism of that phenomenon. Indeed, the critical behaviour related to phase transitions of those ordered phases is expected to be correlated with the superconductivity. In cuprate materials, efforts to find such ordered phases have mainly focused on symmetry breaking in the pseudogap region whereas the Fermi-liquid-like metallic region beyond the so-called critical doping at which the pseudogap disappears has been regarded as a trivial disordered state. Here, we uncover a broken mirror symmetry in the Fermi-liquid-like phase in (Bi,Pb)2Sr2CaCu2O8+δ beyond the critical doping. We do this by tracking the temperature dependence of the rotational-anisotropy of second-harmonic generation for two different dopings. We observe behaviour reminiscent of an order parameter with an onset temperature that coincides with the strange metal to Fermi-liquid-like metal crossover. Angle-resolved photoemission spectroscopy shows that the quasiparticle coherence between CuO2 bilayers is enhanced in proportion to the symmetry-breaking response as a function of temperature, suggesting that the change in metallicity and symmetry breaking are linked. These observations contradict the conventional quantum disordered scenario for over-critical-doped cuprates.
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All relevant data supporting the findings of this study are available from the corresponding authors on reasonable request. Source data are provided with this paper.
References
Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Zaanen, J. From quantum matter to high-temperature superconductivity in copper oxides. Nature 518, 179–186 (2015).
Fradkin, E., Kivelson, S. A. & Tranquada, J. M. Colloquium: theory of intertwined orders in high temperature superconductors. Rev. Mod. Phys. 87, 457 (2015).
Varma, C. M. Colloquium: linear in temperature resistivity and associated mysteries including high temperature superconductivity. Rev. Mod. Phys. 92, 031001 (2020).
Naqib, S., Cooper, J., Tallon, J. & Panagopoulos, C. Temperature dependence of electrical resistivity of high-Tc cuprates—from pseudogap to overdoped regions. Phys. C: Supercond. 387, 365–372 (2003).
Sterpetti, E., Biscaras, J., Erb, A. & Shukla, A. Comprehensive phase diagram of two-dimensional space charge doped Bi2Sr2CaCu2O8+δ. Nat. Commun. 8, 2060 (2017).
Hussey, N. E. Phenomenology of the normal state in-plane transport properties of high-Tc cuprates. J. Phys.: Condens. Matter 20, 123201 (2008).
Cooper, R. et al. Anomalous criticality in the electrical resistivity of La2−xSrxCuO4. Science 323, 603–607 (2009).
Proust, C. & Taillefer, L. The remarkable underlying ground states of cuprate superconductors. Annu. Rev. Condens. Matter Phys. 10, 409–429 (2019).
Xia, J. et al. Polar Kerr-effect measurements of the high-temperature YBa2Cu3O6+x superconductor: evidence for broken symmetry near the pseudogap temperature. Phys. Rev. Lett. 100, 127002 (2008).
Sato, Y. et al. Thermodynamic evidence for a nematic phase transition at the onset of the pseudogap in YBa2Cu3Oy. Nat. Phys. 13, 1074–1078 (2017).
Zhang, J. et al. Discovery of slow magnetic fluctuations and critical slowing down in the pseudogap phase of YBa2Cu3Oy. Sci. Adv. 4, eaao5235 (2018).
Ishida, K. et al. Divergent nematic susceptibility near the pseudogap critical point in a cuprate superconductor. J. Phys. Soc. Jpn 89, 064707 (2020).
Kurashima, K. et al. Development of ferromagnetic fluctuations in heavily overdoped (Bi, Pb)2Sr2CuO6+δ copper oxides. Phys. Rev. Lett. 121, 057002 (2018).
Peng, Y. et al. Re-entrant charge order in overdoped (Bi, Pb)2.12Sr1.88CuO6+δ outside the pseudogap regime. Nat. Mater. 17, 697–702 (2018).
Miao, H. et al. Charge density waves in cuprate superconductors beyond the critical doping. npj Quantum Mater. 6, 31 (2021).
Zhao, L. et al. Evidence of an odd-parity hidden order in a spin–orbit coupled correlated iridate. Nat. Phys. 12, 32–36 (2016).
Harter, J., Zhao, Z., Yan, J.-Q., Mandrus, D. & Hsieh, D. A parity-breaking electronic nematic phase transition in the spin–orbit coupled metal \({{{{\rm{Cd}}}}}_{2}{{{{\rm{Re}}}}}_{2}{{{{\rm{O}}}}}_{7}\). Science 356, 295–299 (2017).
Jin, W. et al. Observation of a ferro-rotational order coupled with second-order nonlinear optical fields. Nat. Phys. 16, 42–46 (2020).
Kim, S. et al. A compact and stable incidence-plane-rotating second harmonics detector. Rev. Sci. Instrum. 92, 043905 (2021).
Zhao, L. et al. A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy. Nat. Phys. 13, 250–254 (2017).
Torre, Adl et al. Mirror symmetry breaking in a model insulating cuprate. Nat. Phys. 17, 777–781 (2021).
Frison, R. et al. Crystal symmetry of stripe-ordered La1.88Sr0.12CuO4. Phys. Rev. B 105, 224113 (2022).
Kan, X. & Moss, S. Four-dimensional crystallographic analysis of the incommensurate modulation in a Bi2Sr2CaCu2O8 single crystal. Acta Crystallogr. Sect. B: Struct. Sci. 48, 122–134 (1992).
Ivanov, A. A. et al. Local noncentrosymmetric structure of Bi2Sr2CaCu2O8+y by X-ray magnetic circular dichroism at Cu K-edge XANES. J. Supercond. Nov. Magn. 31, 663–670 (2018).
Pavlov, V., Pisarev, R., Kirilyuk, A. & Rasing, T. Observation of a transversal nonlinear magneto-optical effect in thin magnetic garnet films. Phys. Rev. Lett. 78, 2004 (1997).
Yang, Z. et al. Thermal expansion of Bi2.2Sr1.8CaCu2Ox superconductor single crystals. J. Supercond. 8, 233–239 (1995).
Kar, U. et al. Nonlinear and nonreciprocal transport effects in untwinned thin films of ferromagnetic Weyl metal SrRuO3. Phys. Rev. X 14, 011022 (2024).
Shai, D. et al. Quasiparticle mass enhancement and temperature dependence of the electronic structure of ferromagnetic SrRuO3 thin films. Phys. Rev. Lett. 110, 087004 (2013).
Kaminski, A. et al. Crossover from coherent to incoherent electronic excitations in the normal state of Bi2Sr2CaCu2O8+δ. Phys. Rev. Lett. 90, 207003 (2003).
Axe, J. et al. Structural phase transformations and superconductivity in La2−xBaxCuO4. Phys. Rev. Lett. 62, 2751 (1989).
Kambe, S., Matsuoka, T., Takahasi, M., Kawai, M. & Kawai, T. Superconductive transition at 98.5 K in monoclinic (Bi, Pb)2Sr2CaCu2Oy. Phys. Rev. B 42, 2669 (1990).
Sarkar, T. et al. Ferromagnetic order beyond the superconducting dome in a cuprate superconductor. Science 368, 532–534 (2020).
Fechner, M., Fierz, M. J., Thöle, F., Staub, U. & Spaldin, N. A. Quasistatic magnetoelectric multipoles as order parameter for pseudogap phase in cuprate superconductors. Phys. Rev. B 93, 174419 (2016).
Lovesey, S., Chatterji, T., Stunault, A., Khalyavin, D. & van der Laan, G. Direct observation of anapoles by neutron diffraction. Phys. Rev. Lett. 122, 047203 (2019).
Wang, C., Nahum, A., Metlitski, M. A., Xu, C. & Senthil, T. Deconfined quantum critical points: symmetries and dualities. Phys. Rev. X 7, 031051 (2017).
Cui, Y. et al. Proximate deconfined quantum critical point in SrCu2(BO3)2. Science 380, 1179–1184 (2023).
Usui, T. et al. Doping dependencies of onset temperatures for the pseudogap and superconductive fluctuation in Bi2Sr2CaCu2O8+δ, studied from both in-plane and out-of-plane magnetoresistance measurements. J. Phys. Soc. Jpn 83, 064713 (2014).
Watanabe, T., Fujii, T. & Matsuda, A. Anisotropic resistivities of precisely oxygen controlled single-crystal Bi2Sr2CaCu2O8+δ: Systematic study on ‘spin gap’ effect. Phys. Rev. Lett. 79, 2113 (1997).
Momma, K. & Izumi, F. Vesta 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44, 1272–1276 (2011).
Fichera, B. ShgPy. GitHub https://bfichera.github.io/shgpy/ (2020).
Acknowledgements
We are grateful to R. Noguchi, S. S. Huh, H. Y. Choi and A. Hallas for their helpful discussions and useful comments. We appreciate the technical support on the fitting process from B. T. Fichera. We also thank S. H. Kim for his contribution to RA-SHG development. This work was conducted under the ISSP-CCES Collaborative Programme and was supported by the Institute for Basic Science in the Republic of Korea (Grant Nos. IBS-R009-G2 and IBSR009-D1). This work was also supported by the National Research Foundation of Korea (Grant Nos. 2022R1A3B1077234 and RS-2023-00258359) and the Japan Society for the Promotion of Science (KAKENHI Grant No. JP19H05823).
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S.J., D.S. and C.K. conceived the central idea and directed the project. S.J. performed the optical measurements with support from B.S., C.R., T.W.N. and S.S. S.J. conducted the symmetry analysis with support from B.S., C.R., Y.K. and S.K. S.J. performed the ARPES measurements with support from D.K. and Y.L. S.J. and D.S. performed the transport measurements. D.S. synthesized and characterized the samples with support from S.I. and H.E. S.J., D.S. and C.K. wrote the paper with input from all the authors.
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Jung, S., Seok, B., Roh, C.j. et al. Spontaneous breaking of mirror symmetry in a cuprate beyond critical doping. Nat. Phys. 20, 1616–1621 (2024). https://doi.org/10.1038/s41567-024-02601-1
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DOI: https://doi.org/10.1038/s41567-024-02601-1