Research ArticlePHYSICS

Nonequilibrium electron and lattice dynamics of strongly correlated Bi2Sr2CaCu2O8+δ single crystals

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Science Advances  27 Apr 2018:
Vol. 4, no. 4, eaap7427
DOI: 10.1126/sciadv.aap7427
  • Fig. 1 Comparison of the MeV-UED and tr-ARPES techniques.

    Schematic of UED (A) and tr-ARPES (B) experiments. (C) Diffraction pattern of the Bi-2212 sample taken by MeV-UED. The inset shows the profile of (040) peak with central Bragg peak (blue) and satellite SL peaks (red). (D) Time-resolved dynamics of electron and phonon systems. Blue (nodal) and red (off-nodal) circles show changes of electron spectral weight obtained by tr-ARPES in different parts of the Brillouin zone. Changes of diffraction peak intensities in the MeV-UED experiment are shown by green (Bragg) and purple (SL) circles. All changes are normalized by the values before the excitation. Solid lines are fits described in Materials and Methods. Dashed lines indicate the arrival of the pump pulse (zero delay) and the turning point in electron and lattice dynamics. The inset shows equilibrium of the Fermi surface. Regions where data were taken are circled. Dotted lines show the underlying tight binding and Yang-Rice-Zhang Fermi surfaces for optimal doping. The intensity of the electron spectra within the measured regions is color-coded. The solid line is the antiferromagnetic zone boundary. MeV-UED data are taken at 30 K, and tr-ARPES data are taken at 125 K.

  • Fig. 2 Role of the Cu-O vibrations and the total phonon bath in peak intensity suppression as a function of wave vector q.

    Experimental SL (A) and Bragg (B) peak intensities I at 0.4 ps (blue squares for SL and pink squares for Bragg) and 12 ps (red circles for SL and green circles for Bragg) after photoexcitation, normalized by values I0 for the unexcited sample, are plotted as functions of q2. Vertical bars represent statistical error, and horizontal bars result from integrating intensities over several neighboring peaks. The sample base temperature is 300 K, and the laser fluence is 10.7 mJ/cm2. The intensities of SL (C) and Bragg (D) peaks for increased vibrational amplitude in the Cu-O plane (blue squares for SL and pink squares for Bragg) only and for additional increase of Debye-Waller factors of all atoms by 50% (red circles for SL and green circles for Bragg) are calculated with Bloch wave approach and normalized by I0 at 300 K parameters. Solid lines present the linear fit for the data. (E) Schematic motion of atoms for the full-breathing and half-breathing phonon modes.

  • Fig. 3 Temperature and fluence dependence of electron and lattice dynamics.

    Values of long time constants Embedded Image are extracted from the MeV-UED as function of sample temperature (A) and laser fluence (B). The dependence indicates that the phonon population growth after +0.5 ps is dominated by phonon-phonon anharmonic decay and not by electron-phonon coupling. (C) Values of the short time constants extracted from the tr-ARPES experimental data and given in the studies of Perfetti et al. (4), Dal Conte et al. (11), and Dakovski et al. (25) as a function of pump laser fluence. The difference in values for the same fluence is more likely attributed to sample variation from cleave to cleave. Gray lines in (B) and (C) are guides to the eye.

  • Fig. 4 Analysis of the TDS intensity dynamics.

    (A to C) TDS images are obtained by subtracting an average diffraction pattern of the unpumped sample from diffraction patterns at certain delays after the pump laser pulse arrival. For each image, the data are binned within a 1-ps window. Dark horizontal lines appear because of the depleted intensity of the Bragg and SL peaks. (D) Difference between (C) and (B). A streak pattern begins to form on top of the diffuse background. Images (A) to (D) share the same range of intensities, color-coded according to the scale on the left. (E) Scheme of energy transfer between electronic and phonon systems upon photoexcitation. The purple curve represents the schematic evolution of the characteristic time scales of the phonon buildup as a function of the phonon energy. (F) Intensity dynamics of TDS of the low-energy optical (blue) and acoustic (red) phonons. The solid lines are single-exponential growth fits. (G) Intensity distribution of TDS due to the acoustic phonons calculated with Eqs. 4 and 5.

  • Fig. 5 Theoretical prediction of electron and lattice dynamics.

    (A) Time evolution of excited electron population ΔN, averaged phonon displacement squared <X2>, and electron excess energy ΔEel above EF obtained by the simulations shows that the electron and the lattice dynamics happen on the same time scale. (B) Dynamics rates, extracted from exponential fit of the data in (A) at every time point, as functions of time for the parameters presented in (A). The simulations show that the rate of the phonon population growth is governed by the rate of the energy exchange between the electron and the phonon. The energy exchange at the subpicosecond time scale is limited to the Cu-O plane, highlighted in the inset.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/4/eaap7427/DC1

    note S1. Bragg and SL intensity dynamics up to 55-ps delay

    note S2. Fluence dependence of Formula

    note S3. MeV-UED measurements with 4.65-eV pump

    note S4. Validity of single inelastic scattering for the TDS analysis

    note S5. TDS dynamics along symmetrical points of a Brillouin zone

    fig. S1. Lattice dynamics at large delays.

    fig. S2. Values of long time constants Formula extracted from the tr-ARPES as function of laser fluence.

    fig. S3. Lattice dynamics after 4.65-eV photon excitation.

    fig. S4. Evolution of the TDS at Y points of the tetragonal Brillouin zone for 30 K (red circles) and 300 K (blue circles) and the exponential growth fits of the data (solid lines).

  • Supplementary Materials

    This PDF file includes:

    • note S1. Bragg and SL intensity dynamics up to 55-ps delay
    • note S2. Fluence dependence of τellong
    • note S3. MeV-UED measurements with 4.65-eV pump
    • note S4. Validity of single inelastic scattering for the TDS analysis
    • note S5. TDS dynamics along symmetrical points of a Brillouin zone
    • fig. S1. Lattice dynamics at large delays.
    • fig. S2. Values of long time constants τellong extracted from the tr-ARPES as function of laser fluence.
    • fig. S3. Lattice dynamics after 4.65-eV photon excitation.
    • fig. S4. Evolution of the TDS at Y points of the tetragonal Brillouin zone for 30 K (red circles) and 300 K (blue circles) and the exponential growth fits of the data (solid lines).

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