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Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states


In the high-transition-temperature (high-Tc) superconductors the pseudogap phase becomes predominant when the density of doped holes is reduced1. Within this phase it has been unclear which electronic symmetries (if any) are broken, what the identity of any associated order parameter might be, and which microscopic electronic degrees of freedom are active. Here we report the determination of a quantitative order parameter representing intra-unit-cell nematicity: the breaking of rotational symmetry by the electronic structure within each CuO2 unit cell. We analyse spectroscopic-imaging scanning tunnelling microscope images of the intra-unit-cell states in underdoped Bi2Sr2CaCu2O8 +δ and, using two independent evaluation techniques, find evidence for electronic nematicity of the states close to the pseudogap energy. Moreover, we demonstrate directly that these phenomena arise from electronic differences at the two oxygen sites within each unit cell. If the characteristics of the pseudogap seen here and by other techniques all have the same microscopic origin, this phase involves weak magnetic states at the O sites that break 90°-rotational symmetry within every CuO2 unit cell.

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Figure 1: CuO 2 electronic structure and ω  ≈  Δ 1 pseudogap states.
Figure 2: Imaging the spatial symmetries of the ω  ≈  Δ 1 pseudogap states.
Figure 3: Nematic ordering and O-site specificity of ω  ≈  Δ 1 pseudogap states.
Figure 4: Rapid increase of correlation length of nematicity at ω  ≈  Δ1.


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We are grateful to P. Abbamonte, D. Bonn, J.C. Campuzano, D.M. Eigler, E. Fradkin, T. Hanaguri, W. Hardy, J. E. Hoffman, S. Kivelson, A.P. Mackenzie, M. Norman, B. Ramshaw, S. Sachdev, G. Sawatzky, H. Takagi, J. Tranquada and J. Zaanen, for discussions and communications. Theoretical studies were supported by NSF DMR-0520404 to the Cornell Center for Materials Research. Experimental studies are supported by the Center for Emergent Superconductivity, an Energy Frontier Research Center, headquartered at Brookhaven National Laboratory and funded by the US Department of Energy, under DE-2009-BNL-PM015, as well as by a Grant-in-Aid for Scientific Research from the Ministry of Science and Education (Japan) and the Global Centers of Excellence Program for Japan Society for the Promotion of Science. A.R.S. acknowledges support from the US Army Research Office. M.J.L., J.C.D. and E.-A.K. thank KITP for its hospitality. J.C.D. acknowledges gratefully the hospitality and support of the Physics and Astronomy Department at the University of British Columbia, Vancouver, Canada.

Author information




M.J.L. and E.-A.K. led the theoretical studies and initially observed the possibility of nematic order in electronic structure images; M.J.L., K.F. and J.P.S. developed the data analysis algorithms and carried out the analysis; K.F., J.L., C.K.K., A.R.S. and Y.K. carried out the experiments and systematic tests; K.F, H.E. and S.U. synthesized the sequence of samples; K.F. was responsible for the figures and SOM; E.-A.K., J.C.D. and M.J.L. supervised the investigation and wrote the paper. The manuscript reflects the contributions of all authors.

Corresponding author

Correspondence to Eun-Ah Kim.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Notes and Data 1-6, Supplementary Figures S1-S6 with legends, and a table showing a list of symbols. (PDF 8808 kb)

Supplementary Movie 1

This movie shows the reduced energy (e) dependence of coarse-grained r-space nematic order parameter ONQ(r,e). The procedure for generating the map of ONQ(r,e) for a given value of e is explained in section VI of the Supplementary Information file (Equation S10) . The movie is referred to in paragraph 12 of the main text. (MOV 141 kb)

Supplementary Movie 2

This movie shows the reduced energy (e) dependence of coarse-grained r-space nematic order parameter OSQ(r,e). The procedure for generating the map of ONQ(r,e) for a given value of e is explained in section VI of the Supplementary Information file (Equation S11). The movie is referred to in paragraph 12 of the main text. (MOV 226 kb)

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Lawler, M., Fujita, K., Lee, J. et al. Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states. Nature 466, 347–351 (2010).

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