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Femtosecond electron-phonon lock-in by photoemission and x-ray free-electron laser

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Science  07 Jul 2017:
Vol. 357, Issue 6346, pp. 71-75
DOI: 10.1126/science.aak9946
  • Fig. 1 Experimental geometry and coherent lattice dynamics.

    (A) FeSe/SrTiO3 films were measured by trXRD and trARPES. Δt denotes the delay of the x-ray (turquoise) and UV (purple) probe pulse with respect to the IR pump pulse (red). (B) X-ray intensity of the (004) Bragg peak as a function of Δt. Photoexcitation (F = 1.83 mJ/cm2) initiates a coherent A1g phonon (left inset), resulting in oscillations of the x-ray signal at the A1g frequency (right inset). FT, Fourier transform; arb. u., arbitrary units. (C) Coherent x-ray signal at T = 20 and 180 K (blue and orange, respectively; raw data are shown in fig. S1) after subtracting a smooth background [dotted black line in (B)]. (D) Dependence of the x-ray signal on the incident fluence at T = 20 K. (E) Corresponding displacement δzSe. Time zero is determined by the exponentially decaying initial intensity drop [dotted black line in (D), convolved with the overall time resolution]. Errors of the frequency in (C) denote 1 standard deviation obtained from the fitting. In (C), (D), and (E), solid black lines indicate fits of the data, and curves are offset for clarity by the amounts indicated in each panel.

  • Fig. 2 Coherent electron dynamics.

    (A) Equilibrium photoemission spectrum at T = 20 K along the Γ-X direction. Electronic band dispersions calculated by DFT are overlaid (renormalized by a factor of 3). Dominant features correspond to one of the dxz/yz bands (orange) and the Embedded Image band (blue). Dashed lines indicate unresolved bands, and solid lines indicate detected bands. (B) Photoinduced shift of the dxz/yz band at four delays, corresponding to extrema of the coherent oscillations [denoted by vertical dashed lines in (C)]. (C and D) Momentum-averaged energy shifts of the dxz/yz and Embedded Image bands, respectively. Solid black lines indicate fits of the data. Traces in (C) and (D) are offset for clarity.

  • Fig. 3 Coherent lock-in at the A1g frequency.

    (A) Oscillations of the selenium displacement δzSe (blue) and the momentum-averaged energy shift Embedded Image (orange and green). trXRD and trARPES data were measured with F = 0.46 and 0.37 mJ/cm2, respectively. Black lines indicate fits of an exponentially decaying cosine with a polynomial background to extract the peak-to-peak oscillation amplitudes ΔzSe and ΔEmbedded Image at time zero. (B) Schematic of the A1g phonon mode (top), which periodically modulates the electronic band energies (bottom). (C and D) Lattice and band oscillation amplitudes as a function of the incident pump fluence. Solid lines indicate linear fits. Error bars in (C) and (D) denote statistical uncertainties, whereas the shaded areas represent systematic fluence uncertainties (supplementary text). The error of the fitted slopes accounts for both statistical and systematic uncertainties.

  • Table 1 Comparison of experiment and theory.

    Shown are selenium height zSe, A1g phonon frequency Embedded Image, and A1g deformation potentials ΔExz/yzzSe and Embedded Image obtained from experiments, canonical DFT calculations, and DFT+DMFT by Mandal et al. (5); for ΔExz/yzzSe, the band-average (maximum) values are displayed. The experimental value for zSe is taken from Margadonna et al. (30), whereas the deformation potentials are obtained by combining the data shown in Fig. 3, C and D, and applying corrections for spatial integration over pump and probe profiles and effective energy densities (supplementary text). The error of the deformation potentials includes systematic and statistical uncertainties. DFT deformation potentials account for an empirical renormalization factor of 3, and the errors reflect the uncertainty of the renormalization determined from ARPES. Theoretical values for Embedded Image are deduced from quadratic fits to the relative total energy.

    ExperimentDFT+DMFT (5)DFT
    zSe (reciprocal lattice units)0.26530.270.2456
    Embedded Image (terahertz)5.30 ± 0.055.76.5 ± 0.3
    ΔExz/yzzSe (millielectron volts per picometer)−13.0 ± 2.5−10.3 (–13.4)−1.6 ± 0.2
    Embedded Image (millielectron volts per picometer)−16.5 ± 3.2No data−8.5 ± 0.9

Supplementary Materials

  • Femtosecond electron-phonon lock-in by photoemission and x-ray free-electron laser

    S. Gerber, S.-L. Yang, D. Zhu, H. Soifer, J. A. Sobota, S. Rebec, J. J. Lee, T. Jia, B. Moritz, C. Jia, A. Gauthier, Y. Li, D. Leuenberger, Y. Zhang, L. Chaix, W. Li, H. Jang, J.-S. Lee, M. Yi, G. L. Dakovski, S. Song, J. M. Glownia, S. Nelson, K. W. Kim, Y.-D. Chuang, Z. Hussain, R. G. Moore, T. P. Devereaux, W.-S. Lee, P. S. Kirchmann, Z.-X. Shen

    Materials/Methods, Supplementary Text, Tables, Figures, and/or References

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    • Materials and Methods
    • Supplementary Text
    • Figs. S1 to S12
    • Table S1
    • References