Mid-infrared resonant excitation of the c-axis-polarized apical-oxygen phonon of underdoped YBa2Cu3O6+x transiently generates c-axis optical properties resembling superconductivity far above the equilibrium transition temperature. Femtosecond X-ray diffraction combined with density functional theory (DFT) determined the transient crystal structure — a staggering of intra- and inter-bilayer Cu–O distances, apical-oxygen displacement, and anisotropic O–Cu–O bond buckling — and DFT further predicted a light-induced charge transfer from the CuO2 planes to the oxygen-deficient Cu–O chains, an enhanced planar orbital character, and possible destabilization of competing charge-density-wave order. The open problem is to turn this LDA-level, indirectly measured picture into a microscopic, quantitatively tested description of the light-induced state: a many-body (beyond-LDA) treatment of the displaced structure; direct experimental measurement of the transient electronic structure, spectral-weight redistribution and actual charge transfer; the interplay with charge-density-wave correlations; and a quantitative microscopic model connecting the specific atomic displacements to the measured changes of the c-axis optical conductivity and interlayer Josephson coupling, disentangling phonon-mediated from direct electronic excitation channels.

Background

YBa2Cu3O6+x (YBCO) is a layered cuprate high-temperature superconductor built from conducting CuO2 bilayers separated by insulating layers containing yttrium, and by Cu–O chains that control the hole doping (the concentration of holes introduced into the CuO2 planes) of the planes. At oxygen content near x = 0.5 (ortho-II order, where full and oxygen-deficient chains alternate), the equilibrium superconducting transition temperature is about 52 K, and the material exhibits the pseudogap regime (a temperature range above the superconducting transition in which the low-energy electronic density of states is partially depleted, without long-range superconducting order) and competing charge-density-wave (CDW) correlations — a periodic modulation of the carrier density in the CuO2 planes that competes with superconductivity. The apical oxygens are the oxygen ions that sit above and below the CuO2 planes, between planes and chains.

Nonlinear phononics is a technique in which an intense mid-infrared pulse resonantly drives an infrared-active lattice vibration; anharmonic (cubic) coupling of this driven mode to Raman-active modes (lattice vibrations that are symmetry-forbidden to absorb infrared light directly) rectifies the oscillatory motion into a quasi-static deformation of the crystal structure that lasts for picoseconds. In YBa2Cu3O6.5 this was done by exciting the 670 cm^-1, c-axis-polarized B1u mode dominated by apical-oxygen motion (Kaiser et al. 2014; Hu et al. 2014). Those terahertz probe experiments found that, in the normal state above the transition temperature, such driving transiently produces c-axis optical properties strongly resembling the superconducting state — a new plasma edge in the reflectivity, associated with the Josephson plasma resonance, i.e. the collective oscillation whose frequency is set by the tunneling (Josephson) coupling of Cooper pairs between adjacent CuO2 layers.

Mankowsky et al. (Nature 516, 71 (2014)) combined femtosecond X-ray diffraction at a free-electron laser (a facility producing ultrashort, intense X-ray pulses) with ab initio density functional theory (DFT, a method that computes electronic structure from the ground-state charge density) to determine the crystal structure of this transient state at 100 K. They found a staggered dilation and contraction of the intra- and inter-bilayer Cu–O distances, a decrease of the apical-oxygen–copper distance, and anisotropic increases of the in-plane O–Cu–O bond buckling. DFT (at the local-density-approximation, LDA, level) indicated dramatic changes of the electronic structure in this displaced geometry: a lowering of the oxygen-deficient-chain bands by tens of meV, reducing their hybridization with the planar copper orbitals — interpreted as charge transfer from the CuO2 planes to the chains — a closing of the chain-derived Fermi-surface pockets, and an enhanced dx2−y2d_{x^2-y^2} orbital character of the planar electronic structure, which the authors argued should favor superconductivity. They also speculated that the Fermi-surface changes might destabilize the competing CDW order, further aiding superconductivity.

The limitation acknowledged in the source paper itself is that cuprates are strongly correlated electron systems, which LDA-level DFT does not describe: a quantitative account of the spectral-weight redistribution, gap structure, and pairing interaction in the light-induced state requires a full many-body treatment, for example dynamical mean-field theory (DMFT, a method in which a lattice model of correlated electrons is mapped onto a self-consistently coupled quantum impurity problem) or cluster extensions. The DFT charge-transfer prediction was at that point supported only by indirect evidence, the CDW destabilization was a conjecture, the microscopic parameters linking the measured atomic displacements to the observed redistribution of intra- and inter-bilayer Josephson coupling in the c-axis optical conductivity were not modeled, and the respective roles of phonon-driven lattice deformation and direct electronic (charge-transfer) excitation by the pump were not disentangled.

Problem Statement

For the transient state of underdoped YBa2Cu3O6.5 (and closely related oxygen contents) generated by resonant mid-infrared excitation of the 670 cm^-1 apical-oxygen phonon, whose crystal structure was determined by Mankowsky et al. (2014), establish a quantitative microscopic characterization and explanation of the light-induced electronic state and of the enhancement of superconducting correlations. Specifically:

(1) Compute the electronic structure of the measured displaced crystal structure beyond the local-density approximation — using a many-body treatment — quantitatively describing the redistribution of spectral weight between CuO2 planes and Cu–O chains, the plane-to-chain charge transfer and the actual transient doping level, the gap structure, and the pairing interaction in the light-induced state.

(2) Measure the transient electronic structure directly — under the resonant phonon drive — to confirm or refute the DFT-level predictions of (1) and determine the light-induced charge redistribution experimentally.

(3) Determine experimentally how the lattice distortion affects competing orders, in particular the charge-density-wave correlations in the CuO2 planes, across the relevant temperature and doping range.

(4) Construct a quantitative microscopic model that derives the observed redistribution of intra- and inter-bilayer Josephson coupling and the changes in the c-axis optical conductivity from the specific light-induced atomic displacements (apical-oxygen shift, O–Cu–O bond buckling, staggered bilayer distances), rather than treating the coupling as an externally modulated parameter.

(5) Disentangle the contributions of the phonon-driven lattice deformation and of direct electronic excitation (charge-transfer excitation at the pump frequency) to the observed non-equilibrium superconducting response, and establish the microscopic origin of the light-enhanced superconducting correlations (including whether they are genuinely superconducting, as suggested by the transient Meissner (magnetic-field-expulsion) response, and by what mechanism the drive enhances or synchronizes them).

These five deliverables are jointly required components of the single objective of understanding, at the microscopic level, how nonlinear lattice excitation produces the observed light-induced state in YBCO, and none of them resolves the question on its own. The required target is the light-induced state at the source composition — underdoped YBa2Cu3O6.5 and closely related oxygen contents, under the conditions at which the transient crystal structure was determined — and the question is resolved when these five components jointly yield a quantitatively consistent microscopic characterization of that target: a beyond-LDA electronic structure that accounts for the directly measured transient electronic structure and charge redistribution, and a microscopic model that derives the measured changes of the c-axis optical conductivity and of the intra- and inter-bilayer Josephson coupling from the measured atomic displacements rather than fitting them. Extending the characterization to other dopings and temperatures extends the same non-equilibrium phase diagram and is not required for resolution, except that deliverable (3) must cover the temperature and doping range over which the light-induced state is observed.

References

  1. R. Mankowsky, A. Subedi, M. Först, S. O. Mariager, M. Chollet, H. T. Lemke, J. S. Robinson, J. M. Glownia, M. P. Minitti, A. Frano, M. Fechner, N. A. Spaldin, T. Loew, B. Keimer, A. Georges, A. Cavalleri, "Nonlinear lattice dynamics as a basis for enhanced superconductivity in YBa2Cu3O6.5", Nature 516, 71–73 (2014), DOI 10.1038/nature13875, https://doi.org/10.1038/nature13875 (arXiv:1405.2266, https://arxiv.org/abs/1405.2266)
  2. S. Kaiser, C. R. Hunt, D. Nicoletti, W. Hu, I. Gierz, H. Y. Liu, M. Le Tacon, T. Loew, D. Haug, B. Keimer, A. Cavalleri, "Optically induced coherent transport far above Tc in underdoped YBa2Cu3O6+δ", Phys. Rev. B 89, 184516 (2014), DOI 10.1103/PhysRevB.89.184516, https://doi.org/10.1103/PhysRevB.89.184516
  3. W. Hu, S. Kaiser, D. Nicoletti, C. R. Hunt, I. Gierz, M. C. Hoffmann, M. Le Tacon, T. Loew, B. Keimer, A. Cavalleri, "Optically enhanced coherent transport in YBa2Cu3O6.5 by ultrafast redistribution of interlayer coupling", Nature Materials 13, 705–711 (2014), DOI 10.1038/nmat3963, https://doi.org/10.1038/nmat3963
  4. A. Subedi, A. Cavalleri, A. Georges, "Theory of nonlinear phononics for coherent light control of solids", Phys. Rev. B 89, 220301(R) (2014), DOI 10.1103/PhysRevB.89.220301, https://doi.org/10.1103/PhysRevB.89.220301
  5. M. Först, A. Frano, S. Kaiser, R. Mankowsky, C. R. Hunt, J. J. Turner, G. L. Dakovski, M. P. Minitti, J. Robinson, T. Loew, M. Le Tacon, B. Keimer, J. P. Hill, A. Cavalleri, S. S. Dhesi, "Femtosecond x rays link melting of charge-density wave correlations and light-enhanced coherent transport in YBa2Cu3O6.6", Phys. Rev. B 90, 184514 (2014), DOI 10.1103/PhysRevB.90.184514, https://doi.org/10.1103/PhysRevB.90.184514
  6. R. Mankowsky, M. Först, A. Cavalleri, "Non-equilibrium control of complex solids by nonlinear phononics", Reports on Progress in Physics 79, 064503 (2016), DOI 10.1088/0034-4885/79/6/064503, https://doi.org/10.1088/0034-4885/79/6/064503
  7. Aavishkar A. Patel, Andreas Eberlein, "Light-induced enhancement of superconductivity via melting of competing bond-density wave order in underdoped cuprates", Phys. Rev. B 93, 195139 (2016), DOI 10.1103/PhysRevB.93.195139, https://doi.org/10.1103/PhysRevB.93.195139
  8. Mehrtash Babadi, Michael Knap, Ivar Martin, Gil Refael, Eugene Demler, "Theory of parametrically amplified electron-phonon superconductivity", Phys. Rev. B 96, 014512 (2017), DOI 10.1103/PhysRevB.96.014512, https://doi.org/10.1103/PhysRevB.96.014512
  9. R. Mankowsky, M. Fechner, M. Först, A. von Hoegen, J. Porras, T. Loew, G. L. Dakovski, M. Seaberg, S. Möller, G. Coslovich, B. Keimer, S. S. Dhesi, A. Cavalleri, "Optically induced lattice deformations, electronic structure changes, and enhanced superconductivity in YBa2Cu3O6.48", Structural Dynamics 4, 044007 (2017), DOI 10.1063/1.4977672, https://doi.org/10.1063/1.4977672
  10. H. Gretarsson, S. M. Souliou, S. Jeong, J. Porras, T. Loew, M. Bluschke, M. Minola, B. Keimer, M. Le Tacon, "Light-induced metastable state in charge-ordered YBa2Cu3O6+x", Phys. Rev. B 98, 075134 (2018), DOI 10.1103/PhysRevB.98.075134, https://doi.org/10.1103/PhysRevB.98.075134
  11. B. Liu, M. Först, M. Fechner, D. Nicoletti, J. Porras, T. Loew, B. Keimer, A. Cavalleri, "Pump Frequency Resonances for Light-Induced Incipient Superconductivity in YBa2Cu3O6.5", Phys. Rev. X 10, 011053 (2020), DOI 10.1103/PhysRevX.10.011053, https://doi.org/10.1103/PhysRevX.10.011053
  12. S. J. Zhang, Z. X. Wang, H. Xiang, X. Yao, Q. M. Liu, L. Y. Shi, T. Lin, T. Dong, D. Wu, N. L. Wang, "Photoinduced Nonequilibrium Response in Underdoped YBa2Cu3O6+x Probed by Time-Resolved Terahertz Spectroscopy", Phys. Rev. X 10, 011056 (2020), DOI 10.1103/PhysRevX.10.011056, https://doi.org/10.1103/PhysRevX.10.011056
  13. M. Altarelli, "Possible experimental test of the nonlinear phononics interpretation of light-induced superconductivity", Phys. Rev. Research 2, 033384 (2020), DOI 10.1103/PhysRevResearch.2.033384, https://doi.org/10.1103/PhysRevResearch.2.033384
  14. Marios H. Michael, Alexander von Hoegen, Michael Fechner, Michael Först, Andrea Cavalleri, Eugene Demler, "Parametric resonance of Josephson plasma waves: A theory for optically amplified interlayer superconductivity in YBa2Cu3O6+x", Phys. Rev. B 102, 174505 (2020), DOI 10.1103/PhysRevB.102.174505, https://doi.org/10.1103/PhysRevB.102.174505
  15. A. von Hoegen, M. Fechner, M. Först, N. Taherian, E. Rowe, A. Ribak, J. Porras, B. Keimer, M. Michael, E. Demler, A. Cavalleri, "Amplification of Superconducting Fluctuations in Driven YBa2Cu3O6+x", Phys. Rev. X 12, 031008 (2022), DOI 10.1103/PhysRevX.12.031008, https://doi.org/10.1103/PhysRevX.12.031008
  16. A. Ribak, M. Buzzi, D. Nicoletti, R. Singla, Y. Liu, S. Nakata, B. Keimer, A. Cavalleri, "Two-fluid dynamics in driven YBa2Cu3O6.48", Phys. Rev. B 107, 104508 (2023), DOI 10.1103/PhysRevB.107.104508, https://doi.org/10.1103/PhysRevB.107.104508
  17. S. Fava, G. De Vecchi, G. Jotzu, M. Buzzi, T. Gebert, Y. Liu, B. Keimer, A. Cavalleri, "Magnetic field expulsion in optically driven YBa2Cu3O6.48", Nature 632, 75–80 (2024), DOI 10.1038/s41586-024-07635-2, https://doi.org/10.1038/s41586-024-07635-2 (arXiv:2405.00848, https://arxiv.org/abs/2405.00848)
  18. Denny Puntel, Dmytro Kutnyakhov, Lukas Wenthaus, Markus Scholz, Nils O. Wind, Michael Heber, Günter Brenner, Genda Gu, Robert J. Cava, Wibke Bronsch, Federico Cilento, Fulvio Parmigiani, Federico Pressacco, "Out-of-equilibrium charge redistribution in a copper-oxide based superconductor by time-resolved X-ray photoelectron spectroscopy", Scientific Reports 14, 8775 (2024), DOI 10.1038/s41598-024-56440-4, https://doi.org/10.1038/s41598-024-56440-4
  19. Sambuddha Chattopadhyay, Christian J. Eckhardt, Dante M. Kennes, Michael A. Sentef, Dongbin Shin, Angel Rubio, Andrea Cavalleri, Eugene A. Demler, Marios H. Michael, "Metastable photo-induced superconductivity far above Tc", npj Quantum Materials 10, 34 (2025), DOI 10.1038/s41535-025-00750-x, https://doi.org/10.1038/s41535-025-00750-x
  20. N. Taherian, M. Först, A. Liu, M. Fechner, D. Pavicevic, A. von Hoegen, E. Rowe, Y. Liu, S. Nakata, B. Keimer, E. Demler, M. H. Michael, A. Cavalleri, "Probing amplified Josephson plasmons in YBa2Cu3O6+x by multidimensional spectroscopy", npj Quantum Materials 10, 54 (2025), DOI 10.1038/s41535-025-00776-1, https://doi.org/10.1038/s41535-025-00776-1
  21. Sujay Ray, Martin Eckstein, Philipp Werner, "Role of the phonon coupling in driving photoexcited Mott insulators towards a transient superconducting state", Phys. Rev. B 111, 174309 (2025), DOI 10.1103/PhysRevB.111.174309, https://doi.org/10.1103/PhysRevB.111.174309 (arXiv:2412.19205, https://arxiv.org/abs/2412.19205)
  22. C. Seo, L. Shen, A. N. Petsch, S. Wandel, V. Esposito, J. D. Koralek, G. L. Dakovski, M.-F. Lin, S. P. Moeller, W. F. Schlotter, A. H. Reid, M. P. Minitti, R. Liang, D. Bonn, W. Hardy, A. Damascelli, C. Giannetti, E. H. da Silva Neto, J. J. Turner, F. Boschini, G. Coslovich, "Persistent short-range charge correlations revealed by ultrafast melting of electronic order in YBa2Cu3O6+x", arXiv:2603.10486 (2026), https://arxiv.org/abs/2603.10486