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Nonlinear lattice dynamics as a basis for enhanced superconductivity in YBa2Cu3O6.5


Terahertz-frequency optical pulses can resonantly drive selected vibrational modes in solids and deform their crystal structures1,2,3. In complex oxides, this method has been used to melt electronic order4,5,6, drive insulator-to-metal transitions7 and induce superconductivity8. Strikingly, coherent interlayer transport strongly reminiscent of superconductivity can be transiently induced up to room temperature (300 kelvin) in YBa2Cu3O6+x (refs 9, 10). Here we report the crystal structure of this exotic non-equilibrium state, determined by femtosecond X-ray diffraction and ab initio density functional theory calculations. We find that nonlinear lattice excitation in normal-state YBa2Cu3O6+x at above the transition temperature of 52 kelvin causes a simultaneous increase and decrease in the Cu–O2 intra-bilayer and, respectively, inter-bilayer distances, accompanied by anisotropic changes in the in-plane O–Cu–O bond buckling. Density functional theory calculations indicate that these motions cause drastic changes in the electronic structure. Among these, the enhancement in the character of the in-plane electronic structure is likely to favour superconductivity.

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Figure 1: Coherent nonlinear lattice dynamics in the limit of cubic coupling.
Figure 2: Structure of YBa2Cu3O6.5.
Figure 3: First-principles calculations of cubic coupling between 11 Ag modes and the driven B1u mode.
Figure 4: Time-dependent diffracted peak intensity (I) for four Bragg reflections.
Figure 5: Transient lattice structure.


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The research leading to these results received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement no. 319286 (QMAC). Funding from the priority program SFB925 of the German Science Foundation is acknowledged. Portions of this research were carried out at the Linac Coherent Light Source (LCLS) at the SLAC National Accelerator Laboratory. The LCLS is an Office of Science User Facility operated for the US Department of Energy Office of Science by Stanford University. This work was supported by the Swiss National Supercomputing Centre under project ID s404. This work was supported by the Swiss National Science Foundation through its National Centre of Competences in Research MUST.

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Authors and Affiliations



A.C. conceived this project. R.M. and M. Först led the diffraction experiment, supported by S.O.M., M.C., H.T.L., J.S.R., J.M.G., M.P.M. and A.F. R.M. and A.S. analysed the data. A.S. performed the DFT calculations, with support from A.G., M. Fechner and N.A.S. The sample was grown by T.L. and B.K. R.M. and A.C. wrote the manuscript, with feedback from all co-authors.

Corresponding authors

Correspondence to R. Mankowsky or A. Cavalleri.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Nonlinear lattice dynamics in the limit of cubic and quartic coupling.

Dashed lines: potential energy of a mode QR as a function of mode amplitude. a, A static distortion shifts the potential of all modes QR that are coupled through a coupling (solid line), displacing the equilibrium position towards a new minimum. b, Owing to quartic coupling, the energy potential of a coupled mode Qj is deformed symmetrically on static distortion . The frequency of the mode first softens until it is destabilized, which manifests in a double well potential (solid line).

Extended Data Figure 2 Changes in diffracted intensity of specific Bragg reflections from fourth-order coupling for different time delays between pump and probe pulse.

We find no evidence of lattice distortions originating from fourth-order contributions to the phonon coupling. The amplitude of the infrared mode QIR is below the threshold beyond which fourth-order effects destabilize coupled phonon modes. Error bars, 1σ (67% confidence interval).

Extended Data Figure 3 Phonon modes of ortho-II YBa2Cu3O6.5.

Sketches of the resonantly excited B1u mode and all 11 Ag modes for which the coupling strengths (Extended Data Table 1) have been calculated.

Extended Data Figure 4 Band structure of the equilibrium (black line) and transient crystal structure.

The band structure is plotted along Γ(0, 0, 0) → X(0.5, 0, 0) → S(0.5, 0.5, 0) → Y(0, 0.5, 0) → Γ(0, 0, 0) → Z(0, 0, 0.5) for transient displaced structures corresponding to amplitudes of 0.8 Å√u (a), which is the amplitude estimated for the geometry of refs 9, 10, and 1.2 Å√u (b).

Extended Data Figure 5 Cuts of the Fermi surface of the equilibrium (black line) and transient crystal structures (red dashed line) at kz = 0.

In the equilibrium structure, the bands of the unfilled-chain Cu atoms give rise to pockets in the Fermi surface. The light-induced displacements shift the densities of states of these bands to lower energies, increasing the filling and reducing the pockets. Above a threshold of 0.8 Å√u, the O-deficient chain bands become fully filled, the pockets close and the Fermi surface consists solely of two-dimensional planar Cu sheets and one-dimensional filled-chain states. The Fermi surface is shown in the displaced state for amplitudes of 0.8 Å√u (left) and 1.2 Å√u (right).

Extended Data Figure 6 Changes in the density of states in the CuO2 plane and the Cu–O chains.

These are obtained from a projection of the density of states onto the copper muffin-tin spheres. a, b, In the light-induced state, the density of states of the O-deficient chain lowers in energy (a), whereas the opposite effect is observed for the Cu in the plane below (b). This corresponds to charge transfer from the planes to the chains. c, d, The density of states of the filled chain Cu is not strongly affected (c). The bands of the planar Cu atoms narrow, which leads to an increase in the density of states near the Fermi level both at sites with filled (d) and empty chains (b). The effect is already visible for a amplitude of 0.3 Å√u (blue) but becomes more prominent for larger displacements of 0.8 Å√u (purple) and 1.2 Å√u (green).

Extended Data Table 1 Mode displacements
Extended Data Table 2 Equilibrium structure of YBa2Cu3O6.5 and light-induced displacements

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Mankowsky, R., Subedi, A., Först, M. et al. Nonlinear lattice dynamics as a basis for enhanced superconductivity in YBa2Cu3O6.5. Nature 516, 71–73 (2014).

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