Ultrafast dynamical Lifshitz transition

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Science Advances  21 Apr 2021:
Vol. 7, no. 17, eabd9275
DOI: 10.1126/sciadv.abd9275
  • Fig. 1 Coulomb-interaction–induced Lifshitz transition in topological Weyl semimetal Td-MoTe2.

    (A) A schematic of the crystal structure of the low-temperature orthorhombic Td-phase of MoTe2 and (B) its associated Brillouin zone (BZ) and surface Brillouin zone (SBZ). (C) The equilibrium phase diagram revealing the effect of the Hubbard Ueff = UJ (J being the Hund’s exchange) on the position of the γ pocket relative to the Fermi energy. The dots are data points obtained from DFT+U simulations, whereas the thick line is a linear fit to the data, serving as a guide to the eye. (D) The electronic band structure of Td-MoTe2 for the equilibrium self-consistently calculated value of Ueff = 2.05 eV (in green) and for the reduced value of Ueff = 0 eV (below the adiabatic Lifshitz transition) and their respective Fermi surface cuts taken at kz = 0 (E and F). In (F), one can clearly see the hallmark of the Coulomb-induced Lifshitz transition—the appearance of γ electron pockets at the Fermi surface.

  • Fig. 2 Ultrafast dynamical Lifshitz transition probed by time-resolved multidimensional photoemission spectroscopy.

    (A) A schematic of the experimental setup featuring infrared (IR) pump/extreme ultraviolet (XUV) probe pulses and a time-of-flight momentum microscope detector allowing for parallel measurement of the band structure of the crystalline solid, as a function of pump-probe time delay (EB, kx, ky, Δt). (B) An example of the experimental 3D volumetric photoemission data, as well as cuts along different high-symmetry directions and cut at the Fermi energy, integrated for all positive time delays. (C to G) Differential (unpumped signal subtracted) 2D Fermi surfaces (kx, ky) as a function of time delay between the IR pump and the XUV probe (integrated more than 400 fs intervals). (H to L) Corresponding raw (right, ky > 0) and differential (left, ky < 0) energy-resolved cuts along Y-Γ-Y (kx = 0).

  • Fig. 3 Ultrafast modification of Hubbard U at the origin of the dynamical Lifshitz transition.

    (A and B) Experimentally measured Fermi surface for t < t0 and t = 500 fs and Fermi surface before and after the pump pulse, obtained by TDDFT+U simulations using the same intensity as in the experiment (I0 = 6.7 × 109 W/cm2). In both cases (theory and experiment), the γ electron pocket close to the Y point, i.e., the hallmark of the Lifshitz transition, is clearly showing up after the interaction with the pump pulse. (C) Normalized laser-assisted photoemission signal (LAPE) (black), normalized γ pocket excited state signal (blue), and energy position of the bottom of the γ pocket (red), as a function of pump-probe delay. The shallow red curve represents the 95% confidence intervals of the γ pocket position extracted from EDC fitting. The dashed red curve serves as a guide to the eye. (D) The vector potential of the laser pulse used in the self-consistent TDDFT+U simulations, with the same wavelength and duration as used in the experiment. (E) Dynamical evolution of Ueff for different laser fluences.

Supplementary Materials

  • Supplementary Materials

    Ultrafast dynamical Lifshitz transition

    Samuel Beaulieu, Shuo Dong, Nicolas Tancogne-Dejean, Maciej Dendzik, Tommaso Pincelli, Julian Maklar, R. Patrick Xian, Michael A. Sentef, Martin Wolf, Angel Rubio, Laurenz Rettig, Ralph Ernstorfer

    Download Supplement

    This PDF file includes:

    • Additional experimental data
    • Adiabatic Lifshitz transition
    • Nonequilibrium Fermi surface
    • Effect of dynamical U
    • Note on the role of dynamical populations
    • Band structure of 1T′-MoTe2
    • Figs. S1 to S6
    • References

    Files in this Data Supplement:

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