Research ArticleCONDENSED MATTER PHYSICS

Ultrafast electron calorimetry uncovers a new long-lived metastable state in 1T-TaSe2 mediated by mode-selective electron-phonon coupling

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Science Advances  01 Mar 2019:
Vol. 5, no. 3, eaav4449
DOI: 10.1126/sciadv.aav4449
  • Fig. 1 Ultrafast electron calorimetry can measure the dynamic electron temperature and band structure to uncover a new long-lived metastable state mediated by mode-selective electron-phonon coupling.

    The upper left panel shows the top view of the Ta plane in 1T-TaSe2. In the CDW state, displacement of the Ta atoms leads to a Embedded Image superstructure consisting of 13-atom star-of-David clusters. After laser excitation, the evolution of the sample is determined first by the electron temperature and then by electron-phonon coupling, which depends on the fluence. For strong laser excitation, the electron-phonon coupling switches from nearly homogeneous to mode selective. The resulting inhomogeneity within the phonon bath drives the material into a new long-lived metastable CDW state. The blue shading represents the electron density in the real space, the gray circles represent Ta atoms, and both amplitudes are exaggerated for better visualization. Te, Tp, and Tl refer to the temperatures of the electron, strongly coupled phonons, and the rest of the phonon bath, respectively. f(E), Fermi-Dirac function.

  • Fig. 2 Evolution of the electron temperature and sudden change in the electron-phonon coupling.

    (A) Photoemission spectra along the Γ-M direction before and after (350 fs) laser excitation with a fluence of 0.86 mJ/cm2. The disappearance of band folding and the CDW gap clearly suggest the collapse of the CDW order. (B) Temporal evolution of the electron temperature Te at a fluence of 0.69 mJ/cm2. The red curve is the two-exponential fit to the data. (C) Calculated charge densities (red) in a star-of-David integrated over the energy windows on the occupied (EF − 1 eV, EF) and unoccupied (EF + 0.2 eV, EF + 1.2 eV) sides. (D) Electron temperature dynamics as a function of laser fluence. (E) Te at 4 ps, when the electron bath is nearly in equilibrium with part of the phonon bath (Tp). The error bars represent the measurement uncertainties. For F < Fc, this quasi-equilibrium temperature reaches the expected value in thermal equilibrium, as indicated by the solid red curve. However, for F > Fc, the temperature abruptly increases above the red curve, indicating a step decrease in the effective heat capacity—only a subset of phonons are strongly coupled to the hot electrons.

  • Fig. 3 Electronic band dynamics and the metastable state.

    (A) Time-dependent photoemission spectrum at the momentum k// as indicated by the vertical dashed line in Fig. 2A. The black dots represent the band positions. (B) Energy shift of the band shown in (A) at two representative laser fluences. Red curves indicate fits of the data, and blue curves indicate the quasi-equilibrium coordinate Q0 as described in the main text. (C) Extracted oscillation frequency f and damping constant γ as a function of fluence. (D) Peak of band shift, peak of Q0, and band shift at 4 ps as a function of fluence. The arrow indicates the saturation value corresponding to melting of the CDW order. At fluences higher than 0.7 mJ/cm2, the material evolves into a new long-lived metastable state. (E and F) Comparison between the evolution of Te and the band shift as a function of fluence. (G) Decay time scales of Te and the band shift as a function of fluence. When F > Fc, the faster decay of Te indicates an enhancement in the averaged electron-phonon coupling, while the decay of band shift starts to deviate from the former and becomes slower. The error bars include the measurement uncertainties and the SD of the fitting.

  • Fig. 4 Experimental band shift (order parameter) as a function of time delay and laser fluence.

    At fluences higher than Fc (~0.7 mJ/cm2 indicated by the red line), the material suddenly evolves into a new metastable state that is distinct from either of the equilibrium phases. Te, Tp, and Tl refer to the temperatures of the electron, strongly coupled phonons, and the rest of the phonon bath, respectively.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/3/eaav4449/DC1

    Section S1. Data analysis of trARPES spectra

    Section S2. DFT calculations of electronic structure

    Section S3. Evolution of the electron temperature

    Section S4. The electronic band shift and the new metastable states

    Section S5. Relationship between the band shift and the CDW order

    Section S6. Caption of the supplementary movie

    Fig. S1. Fit of the trARPES spectra.

    Fig. S2. Band structure for 1T-TaSe2 in the metallic state (1 × 1) with spin-orbit coupling.

    Fig. S3. Partial density of states projected onto three kinds of Ta atoms in the CDW state (Formula) with spin-orbit coupling.

    Fig. S4. Analysis of the electron temperature.

    Fig. S5. Analysis of the band shift.

    Fig. S6. Schematic of the new long-lived metastable state mediated by mode-selective electron-phonon coupling.

    Fig. S7. The long-lasting metastable state.

    Fig. S8. ARPES spectra at selected time delays for the laser fluence of 0.86 mJ/cm2.

    Fig. S9. ARPES spectra at two time delays as a function of laser fluence.

    Movie S1. Transforming a material into a new state after heating the electrons with an ultrafast laser.

    References (4651)

  • Supplementary Materials

    The PDF file includes:

    • Section S1. Data analysis of trARPES spectra
    • Section S2. DFT calculations of electronic structure
    • Section S3. Evolution of the electron temperature
    • Section S4. The electronic band shift and the new metastable states
    • Section S5. Relationship between the band shift and the CDW order
    • Section S6. Caption of the supplementary movie
    • Fig. S1. Fit of the trARPES spectra.
    • Fig. S2. Band structure for 1T-TaSe2 in the metallic state (1 × 1) with spin-orbit coupling.
    • Fig. S3. Partial density of states projected onto three kinds of Ta atoms in the CDW state ( 13×13) with spin-orbit coupling.
    • Fig. S4. Analysis of the electron temperature.
    • Fig. S5. Analysis of the band shift.
    • Fig. S6. Schematic of the new long-lived metastable state mediated by mode-selective electron-phonon coupling.
    • Fig. S7. The long-lasting metastable state.
    • Fig. S8. ARPES spectra at selected time delays for the laser fluence of 0.86 mJ/cm2.
    • Fig. S9. ARPES spectra at two time delays as a function of laser fluence.
    • Legend for movie S1
    • References (4651)

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). Transforming a material into a new state after heating the electrons with an ultrafast laser.

    Files in this Data Supplement:

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