Abstract
Unconventional superconductivity often couples to other electronic orders in a cooperative or competing fashion. Identifying external stimuli that tune between these two limits is of fundamental interest. Here, we show that strain perpendicular to the copper-oxide planes couples directly to the competing interaction between charge stripe order and superconductivity in La1.88Sr0.12CuO4 (LSCO). Compressive c-axis pressure amplifies stripe order within the superconducting state, while having no impact on the normal state. By contrast, strain dramatically diminishes the magnetic field enhancement of stripe order in the superconducting state. These results suggest that c-axis strain acts as tuning parameter of the competing interaction between charge stripe order and superconductivity. This interpretation implies a uniaxial pressure-induced ground state in which the competition between charge order and superconductivity is reduced.
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Introduction
Electronic phases may coexist microscopically, either in a collaborative or competing manner. In elementary chromium, for example, spin and charge density wave orders collaboratively coexist with commensurate ordering vectors1,2,3. A similar spin-charge intertwined order is found in doped lanthanum-based (La-based) cuprate superconductors4,5,6,7,8. Competing interaction is often found in the context of unconventional superconductivity. For example, in kagome metals9,10, pnictides11,12,13, and heavy Fermion systems14, superconductivity can be optimized through the suppression of charge or spin density wave orders.
However, an interplay between density waves and superconductivity – at least theoretically – can lead to a collaborative state. This state would be characterized by a spatially modulated Cooper pair density with a commensurate wave vector. Extensive experimental and theoretical efforts have been devoted to study this novel superconducting state15. Theory works have predicted a connection between superconductivity and stripe order through a so-called pair density wave16. Signatures of these pair density waves have been reported by scanning tunneling microscopy17, but direct diffraction evidence is still missing. A general challenge is therefore to switch the coupling between superconductivity and charge order from competing to collaborative. Ideally, an external stimulus would tune the coupling between these two phases.
Here, using high-energy x-ray diffraction, we show how compressive c-axis uniaxial pressure, perpendicular to the copper-oxide planes, enhances stripe order inside the superconducting state of La1.88Sr0.12CuO4 (LSCO), while charge order remains unchanged in the normal state. We furthermore discover that the magnetic field enhancement of charge order inside the superconducting state is dramatically reduced upon compressive c-axis strain application. This observation suggests a correspondingly reduced phase competition. We thus demonstrate that c-axis pressure acts directly on the coupling between charge stripe order and superconductivity.
Results
X-ray methodology
Stripe charge order in La-based cuprates manifests itself by weak reflections at Qco = τ+(δ, 0, 0.5) where τ represents fundamental Bragg peaks and δ ≈ 1/4 is the stripe incommensurability6,7,18,19. We adopted an x-ray transmission geometry with crystalline a- and c-axes spanning the horizontal scattering plane as illustrated in Fig. 1a. Magnetic field and uniaxial pressure were applied along the c-axis direction.
Uniaxial pressure application
The strain as a result of uniaxial c-axis pressure can be directly estimated from lattice parameter measurements. Pressure-induced compression of the c-axis lattice parameter is evidenced by a shift of (0, 0, n) Bragg peaks to larger scattering angles. Precise strain characterization utilizes multiple such Bragg peaks with n being an even integer (see Method section and Fig. 1b). The resulting c-axis lattice parameter for strained and unstrained LSCO is exemplified in Fig. 1b. As expected, the uniaxial c-axis pressure reduces the c-axis lattice parameter that in turn lowers the superconducting transition temperature Tc20,21,22. Using polarized neutron scattering we confirmed the decrease of Tc with compressive c-axis strain23,24,25,26 – see Fig. 1c and Method section. Exploiting that the lower critical field for superconductivity Hc1 is low, we track the excess depolarisation of the neutron beam due to flux trapped along the c-axis after field-cooling through Tc. The in-plane polarized neutrons are depolarized by this trapped flux. Upon crossing Tc, the flux is released.
Uniaxial c-axis strain effects on charge order
X-ray diffraction intensity was collected using a two-dimensional single-photon detector. Detector regions-of-interest (ROI) are defined such that the signal or background of interest is covered (see Supplementary Fig. 1). We constructed standard one-dimensional rocking curves (see Fig. 1d for Qco = (δ, 0, 12.5)). An advantage of 2D-detectors (over point detectors) is that a background can be estimated by slightly shifting the ROI (grey data in Fig. 1d).
In Fig. 2, we show scans through Qco = (δ, 0, 12.5) and (δ, 0, 16.5), with and without uniaxial c-axis pressure. Data for a La2−xSrxCuO4 crystal with slightly different do** are shown in Supplementary Fig. 2. Intensities and fits are presented after subtracting the background. In the normal state (T > Tc), no pressure effect on charge stripe order is observed. Further, we find a significant pressure-induced enhancement of the charge order reflection inside the superconducting state. The correlation length and incommensurability δ remain virtually unaffected by uniaxial pressure. Observed shifts are within the error bars and thus negligible. From here, we therefore consider the charge order peak amplitude as a function of temperature, uniaxial c-axis pressure, and magnetic field. The peak amplitude Ico is extracted by fitting intensity profiles with a split-normal distribution on a linear background – see Figs. 1d and 2, Supplementary Fig. 3 and Methods.
The temperature dependence of the charge order amplitude is shown in Fig. 3a for strained and unstrained conditions. In the absence of a magnetic field, compressive c-axis pressure enhances the charge order inside the superconducting state. The charge order peak amplitude, due to phase competition19, displays a cusp at Tc. The cusp is shifted to slightly lower temperatures upon application of c-axis pressure. Assuming phase competition between charge order and superconductivity, this suggests a reduction of the superconducting transition temperature, in agreement with the measurements in Fig. 1c. At our base temperature (T = 10 K), the relative peak amplitude, Ico(10 K)/Ico(30 K), scales approximately linearly with the applied strain εc (see Fig. 3b). Within the examined range of εc, the charge order peak amplitude increases by about 25%.
Magnetic field effect
Without strain, magnetic field effects on charge and spin order inside the superconducting state have already been studied\({p}_{0}\cdot \tanh (T-{T}_{c})+{p}_{1}\). The resulting Tc of the zero-pressure LSCO crystal is in accord with the transition temperature obtained from a magnetic susceptibility measurement of the rod (see Supplementary Fig. 8).
Data availability
Data are available upon request.
Code availability
Code is available upon request.
References
Gibbs, D., Mohanty, K. M. & Bohr, J. High-resolution x-ray-scattering study of charge-density-wave modulation in chromium. Phys. Rev. B 37, 562–564 (1988).
Jiang, X. W. & Fishman, R. S. Coupled spin- and charge-density waves in chromium alloys. J. Phys.: Condens. Matter 9, 3417 (1997).
Hu, Y. et al. Real-space observation of incommensurate spin density wave and coexisting charge density wave on Cr (001) surface. Nat. Commun. 13, 445 (2022).
Tranquada, J. M., Buttrey, D. J., Sachan, V. & Lorenzo, J. E. Simultaneous ordering of holes and spins in La2NiO4.125. Phys. Rev. Lett. 73, 1003–1006 (1994).
Tranquada, J. M. et al. Neutron-scattering study of stripe-phase order of holes and spins in La1.48Nd0.4Sr0.12CuO4. Phys. Rev. B 54, 7489–7499 (1996).
Hücker, M. et al. Stripe order in superconducting La2−xBaxCuO4 (0.095 ⩽ x ⩽ 0.155). Phys. Rev. B 83, 104506 (2011).
Thampy, V. et al. Rotated stripe order and its competition with superconductivity in La1.88Sr0.12CuO4. Phys. Rev. B 90, 100510(R) (2014).
Achkar, A. J. et al. Nematicity in stripe-ordered cuprates probed via resonant x-ray scattering. Science 351, 576–578 (2016).
Yu, F. H. et al. Unusual competition of superconductivity and charge-density-wave state in a compressed topological kagome metal. Nat. Commun. 12, 3645 (2021).
Song, Y. et al. Competition of superconductivity and charge density wave in selective oxidized CsV3Sb5 thin flakes. Phys. Rev. Lett. 127, 237001 (2021).
Nandi, S. et al. Anomalous suppression of the orthorhombic lattice distortion in superconducting \({{{{{{{\rm{Ba}}}}}}}}{({{{{{{{{\rm{Fe}}}}}}}}}_{1-x}{{{{{{{{\rm{Co}}}}}}}}}_{x})}_{2}{{{{{{{{\rm{As}}}}}}}}}_{2}\) single crystals. Phys. Rev. Lett. 104, 057006 (2010).
Hu, D. et al. Uniaxial c-axis pressure effects on the underdoped superconductor \({{{{{{{{\rm{BaFe}}}}}}}}}_{2}{({{{{{{{{\rm{As}}}}}}}}}_{0.72}{{{{{{{{\rm{P}}}}}}}}}_{0.28})}_{2}\). Phys. Rev. B 101, 020507 (2020).
Allred, J. M. et al. Coincident structural and magnetic order in \({{{{{{{{\rm{bafe}}}}}}}}}_{2}{({{{{{{{{\rm{As}}}}}}}}}_{1-x}{{{{{{{{\rm{P}}}}}}}}}_{x})}_{2}\) revealed by high-resolution neutron diffraction. Phys. Rev. B 90, 104513 (2014).
Flouquet, J. et al. Trends in heavy fermion matter. J. Phys.: Conf. Ser. 273, 012001 (2011).
Agterberg, D. F. et al. The physics of pair-density waves: Cuprate superconductors and beyond. Annu. Rev. Condens. Matter Phys. 11, 231–270 (2020).
Wang, Y. et al. Pair density waves in superconducting vortex halos. Phys. Rev. B 97, 174510 (2018).
Dai, Z., Zhang, Y.-H., Senthil, T. & Lee, P. A. Pair-density waves, charge-density waves, and vortices in high-Tc cuprates. Phys. Rev. B 97, 174511 (2018).
Tranquada, J. M., Sternlieb, B. J., Axe, J. D., Nakamura, Y. & Uchida, S. Evidence for stripe correlations of spins and holes in copper oxide superconductors. Nat. (Lond.) 375, 561–563 (1995).
Croft, T. P., Lester, C., Senn, M. S., Bombardi, A. & Hayden, S. M. Charge density wave fluctuations in La2−xSrxCuO4 and their competition with superconductivity. Phys. Rev. B 89, 224513 (2014).
Pavarini, E., Dasgupta, I., Saha-Dasgupta, T., Jepsen, O. & Andersen, O. K. Band-structure trend in hole-doped cuprates and correlation with \({T}_{c\max }\). Phys. Rev. Lett. 87, 047003 (2001).
Gugenberger, F. et al. Uniaxial pressure dependence of tc from high-resolution dilatometry of untwinned La2−xSrxCuO4 single crystals. Phys. Rev. B 49, 13137–13142 (1994).
Jalekeshov, A. & Yavidov, B. On the uniaxial strain (pressure) derivatives of the critical temperature of superconductivity of La2−xSrxCuO4. Phys. C: Superconductivity its Appl. 604, 1354177 (2023).
Nakamura, F. et al. Tc enhancement in La2−xSrxCuO4 under anisotropic pressure. J. Low. Temp. Phys. 117, 1145–1149 (1999).
Sato, H. & Naito, M. Increase in the superconducting transition temperature by anisotropic strain effect in (001) La1.85Sr0.15CuO4 thin films on LaSrAlO4 substrates. Phys. C: Superconductivity 274, 221–226 (1997).
Locquet, J. & Williams, E. Epitaxially Induced Defects in Sr- and O-doped La2CuO4 Thin Films Grown by MBE: Implications for Transport Properties. Acta Phys. Pol. A 92, 69–84 (1997).
Takeshita, N., Sasagawa, T., Sugioka, T., Tokura, Y. & Takagi, H. Gigantic anisotropic uniaxial pressure effect on superconductivity within the CuO2 plane of La1.64Eu0.2Sr0.16CuO4: Strain control of stripe criticality. J. Phys. Soc. Jpn. 73, 1123–1126 (2004).
Christensen, N. B. et al. Bulk charge stripe order competing with superconductivity in La2−xSrxCuO4 (x = 0.12). ar**v:1404.3192. https://arxiv.org/abs/1404.3192. (2014).
Choi, J. et al. Unveiling unequivocal charge stripe order in a prototypical cuprate superconductor. Phys. Rev. Lett. 128, 207002 (2022).
Chang, J. et al. Tuning competing orders in La2−xSrxCuO4 cuprate superconductors by the application of an external magnetic field. Phys. Rev. B 78, 104525 (2008).
Lake, B. et al. Antiferromagnetic order induced by an applied magnetic field in a high-temperature superconductor. Nature 415, 299–302 (2002).
Hücker, M. et al. Enhanced charge stripe order of superconducting La2−xBaxCuO4 in a magnetic field. Phys. Rev. B 87, 014501 (2013).
Khaykovich, B. et al. Field-induced transition between magnetically disordered and ordered phases in underdoped La2−xSrxCuO4. Phys. Rev. B 71, 220508 (2005).
Wen, J.-J. et al. Enhanced charge density wave with mobile superconducting vortices in La1.885Sr0.115CuO4. Nat. Commun. 14, 733 (2023).
Demler, E., Sachdev, S. & Zhang, Y. Spin-ordering quantum transitions of superconductors in a magnetic field. Phys. Rev. Lett. 87, 067202 (2001).
Lake, B. et al. Spins in the vortices of a high-temperature superconductor. Science 291, 1759–1762 (2001).
Wu, T. et al. Emergence of charge order from the vortex state of a high-temperature superconductor. Nat. Commun. 4, 2113 (2013).
Nakamura, F. et al. Role of two-dimensional electronic state in superconductivity in La2−xSrxCuO4. Phys. Rev. B 61, 107–110 (2000).
Matt, C. E. et al. Direct observation of orbital hybridisation in a cuprate superconductor. Nat. Commun. 9, 972 (2018).
Kramer, K. P. et al. Band structure of overdoped cuprate superconductors: Density functional theory matching experiments. Phys. Rev. B 99, 224509 (2019).
Sakakibara, H., Usui, H., Kuroki, K., Arita, R. & Aoki, H. Two-Orbital Model Explains the Higher Transition Temperature of the Single-Layer Hg-Cuprate Superconductor Compared to That of the La-Cuprate Superconductor. Phys. Rev. Lett. 105, 057003 (2010).
Sakakibara, H., Usui, H., Kuroki, K., Arita, R. & Aoki, H. Origin of the material dependence of Tc in the single-layered cuprates. Phys. Rev. B 85, 064501 (2012).
Koike, Y. et al. Inhomogeneous superconductivity in both underdoped and overdoped regimes of high-Tc cuprates. J. Phys.: Conf. Ser. 108, 012003 (2008).
P., B. & Segre, C. http://www.csrri.iit.edu/mucal.html. Accessed: 2024-02-06. (2020).
McMaster, W. H., del Grande, N. K., Mallett, J. H. & Hubbell, J. H. Compilation of x-ray cross sections ucrl-50174, sections i, ii revision 1, iii, iv*. Lawrence Livermore National Laboratory Report UCRL-50174 (section I 1970, section II 1969, section III 1969 and section IV 1969) (1970).
Simutis, G. et al. Single-domain stripe order in a high-temperature superconductor. Commun. Phys. 5, 296 (2022).
Jacobsen, H. et al. Neutron scattering study of spin ordering and stripe pinning in superconducting La1.93Sr0.07CuO4. Phys. Rev. B 92, 174525 (2015).
Horibe, Y., Inoue, Y. & Koyama, Y. Direct observation of dynamic local structure in La2−xSrxCuO4 around x = 0.12. Phys. Rev. B 61, 11922–11927 (2000).
Frison, R. et al. Crystal symmetry of stripe-ordered la1.88sr0.12cuo4. Phys. Rev. B 105, 224113 (2022).
Janoschek, M., Klimko, S., Gähler, R., Roessli, B. & Böni, P. Spherical neutron polarimetry with mupad. Phys. B: Condens. Matter 397, 125–130 (2007).
Acknowledgements
J.K., R.F., L.M., D.B., and J.C. acknowledge support Science Foundation (grant no. 501100001711-188564). J.K. is further supported by the PhD fellowship from the German Academic Scholarship Foundation. I.B. acknowledges support from the Swiss Government Excellence Scholarship. Q.W. is supported by the Research Grants Council of Hong Kong (ECS No. 24306223), and the CUHK Direct Grant (No. 4053613). N.B.C was supported by the Danish National Council for Research infrastructure (NUFI) through DANSCATT and the ESS-Lighthouse Q-MAT. This research was carried out at beamline P21.1 at DESY, a member of the Helmholtz Association (HGF). We would like to thank Philipp Glaevecke for technical assistance during the experiment. The research leading to this result has been supported by the project CALIPSOplus under the Grant Agreement 730872 from the EU Framework Programme for Research and Innovation HORIZON 2020. Part of the research have been carried out at the TASP endstation of the spallation source SINQ (PSI).
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T.K., N.M., M.O. grew and J.K. prepared the LSCO crystals. J.Choi, D.B., M.J. designed and tested the pressure cells. X-ray diffraction experiments were carried out by J.K., R.F., A.M., O.I., Mv.Z., N.B.C., Q.W., J.Chang. Polarized neutron scattering experiments were conducted by J.K., N.B.C., D.G.M., G.S., A.A.T., L.T., D.W.T. J.K. carried out the data analysis with input from I.B., Q.W., and L.M.; The project was conceived by J.K. and J.Chang who also wrote the manuscript with input from all authors.
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Küspert, J., Biało, I., Frison, R. et al. Engineering phase competition between stripe order and superconductivity in La1.88Sr0.12CuO4. Commun Phys 7, 225 (2024). https://doi.org/10.1038/s42005-024-01699-2
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DOI: https://doi.org/10.1038/s42005-024-01699-2
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